vedāvināśinaḿ nityaḿ
ya enam ajam avyayam
kathaḿ sa puruṣaḥ pārtha
kaḿ ghātayati hanti kam

Translation of Bhagavad Gita 2.21

O Partha, how can a person who knows that the soul is indestructible, eternal, unborn and immutable kill anyone or cause anyone to kill?

Commentary by Sri A.C. Bhaktivedanta Swami Prabhupada of Gaudiya Sampradaya:

Everything has its proper utility, and a man who is situated in complete knowledge knows how and where to apply a thing for its proper utility. Similarly, violence also has its utility, and how to apply violence rests with the person in knowledge. Although the justice of the peace awards capital punishment to a person condemned for murder, the justice of the peace cannot be blamed, because he orders violence to another person according to the codes of justice. In Manu-samhita, the lawbook for mankind, it is supported that a murderer should be condemned to death so that in his next life he will not have to suffer for the great sin he has committed.

Therefore, the king’s punishment of hanging a murderer is actually beneficial. Similarly, when Krishna orders fighting, it must be concluded that violence is for supreme justice, and thus Arjuna should follow the instruction, knowing well that such violence, committed in the act of fighting for Krishna, is not violence at all because, at any rate, the man, or rather the soul, cannot be killed; so for the administration of justice, so-called violence is permitted. A surgical operation is not meant to kill the patient, but to cure him. Therefore the fighting to be executed by Arjuna at the instruction of Krishna is with full knowledge, so there is no possibility of sinful reaction.Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

With this knowledge, neither you who are fighting nor I who am urging you to fight have any fault. Here nityam is used as an, adverb: “He who knows constantly that the soul is indestructible, unborn, and eternal….”

The words describing the soul are used to negate the objections of Arjuna about destruction. “Whom do I (sa purusah), the Lord, cause to be killed (by advising you to fight)? And how do I cause anyone to be killed? And whom do you kill? And how do you kill?”

Commentary by Sri Ramanuja of Sri Sampradaya:

2.21 He who knows the self to be eternal, as It is indestructible, unborn and changeless — how can that person be said to cause the death of the self, be it of the self existing in the bodies of gods or animals or immovables? Whom does he kill? The meaning is — how can he destroy any one or cause anyone to slay? How does he become an instrument for slaying? The meaning is this: the feeling of sorrow: ‘I cause the slaying of these selves, I slay these,’ has its basis solely in ignorance about the true nature of the self. Let it be granted that what is done is only separation of the bodies from the eternal selves. Even then, when the bodies, which are instruments for the experience of agreeable pleasures, perish, there still exists reason for sorrow in their separation from the bodies. To this (Sri Krsna) replies:
Commentary by Sri Sridhara Swami of Rudra Sampradaya:

The denial of any possibility in the slaying of any living entity has been established, for all living entities continually maintain their existence through the agency of the immortal soul. Who can that person slay and how? When knowing its eternality which is free from modification, its immutability which is free from decay, unborn being free from birth and indestructible being free from death. For it is impossible to destroy the immortal soul by any means. So who then can factually claim to be the cause of another perishing? There is none who can claim this or by any means achieve this. So the Supreme Lord by clarifying this point is also informing Arjuna to that He is not directing him to slay anyone because the soul is factually never slain.
Commentary by Sri Madhvacharya of Brahma Sampradaya:

One who understands that the eternal soul is incapable of being destroyed who can be slain and how? The word avinasinam means indestructible, nityam means eternal and therefore by its own inherent nature the immortal soul is imperishable without any defects because what is eternal is never in a state of modification. The word defect is commonly used for that which is not of perfection. The physical body of the living entities is not perfect it is defective, thus the word destruction is applicable to the physical body but never to the eternal soul.

Now begins the summation.

The word avinasinam is indicative of one whose body is indestructible. Eternal in form only applies to the Supreme Lord. Unlimited activity is the attribute of being independent, total independence is found only in the case of the Supreme Lord, who being immutable is without any support outside of Himself.
Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

As to remove any doubts concerning the Vedic injunction against the killing of cows and the killing of a brahmana such as Drona, the perpetrators of these heinious crimes go directly to hell to suffer at the termination of their material existence. To mitigate this Lord Krishna tells Arjuna that one who knows the soul to be indestructible and thus eternal as well as unborn and unmodifiable although uniquely different within every body knows that no one in anyway can cause the destruction of the soul. Who is the doer in the action of killing? Whom can one cause to be killed? Can one be the agent in the death of the soul? The answer is no to all and it is indicated that there should be no doubt about the veracity of the Vedic scriptures regarding the sin incurred either when one causes another to be killed or when one is directed to kill another. By this the Vedic injunctions prohibiting cow slaughter and the slaying of brahmanas and the great sin attached thereof must be accepted as fact even though one is in knowledge about the factual nature of the eternal reality of the souls immortality.
Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

2.21 In the mantra, ‘He who thinks of this One as the killer,’ having declared that (the Self) does not become the agent or the object of the actof killing, and then in the mantra, ‘Never is this One born,’ etc., having stated the reasons for (Its) changelessness, the Lord sums up the purport of what was declared above: He who knows this One as indestructible, etc. Yah, he who; veda, knows — yah is to be thus connected with Veda –; enam, this One, possessing the characteristics stated in the earlier mantra; as avinasinam, indestructible, devoid of the final change of state; nityam, eternal, devoid of transformation; ajam, birthless; and avyayam, undecaying; katham, how, in what way; (and kam, whom;) does sah, that man of realization; purusah, the person who is himself an authority [i.e. above all injunctions and prohibitions. See 18.16.17.-Tr.]; hanti, kill, undertake the act of killing; or how ghatayati, does he cause (others) to be killed, (how does he) instigate a killer! The intention is to deny both (the acts) by saying, ‘In no way does he kill any one, nor does he cause anyone to be killed’, because an interrogative sense is absurd (here). Since the implication of the reason [The reason for the denial of killing etc. is the changelessness of the Self, and this reason holds good with regard to all actions of the man of realization.-Tr.], viz the immutability of the Self, [The A.A. omits ‘viz the immutability of the Self’.-Tr.] is common (with regard to all actions), therefore the negation of all kinds of actions in the case of a man of realization is what the Lord conveys as the only purport of this context. But the denial of (the act of) killing has been cited by way of an example. Objection: By noticing what special reason for the impossibility of actions in the case of the man of realization does the Lord deny all actions (in his case) by saying, ‘How can that person,’ etc.? Vedantin: Has not the immutability of the Self been already stated as the reason [Some readings omit this word.-Tr.] , the specific ground for the impossibility of all actions? Objection: It is true that it has been stated; but that is not a specific ground, for the man of realization is different from the immutable Self. Indeed, may it not be argued that action does not become impossible for one who has known as unchanging stump of a tree?! Vedantin: No, because of man of Knowledge is one with the Self. Enlightenment does not belong to the aggregate of body and senses. Therefore, as the last laternative, the knower is the Immutable and is the Self which is not a part of the aggregate. Thus, action being impossible for that man of Knowledge, the denial in, ‘How can that person…,’ etc. is reasonable. As on account of the lack of knowledge of the distinction between the Self and the modifications of the intellect, the Self, though verily immutable, is imagined through ignorance to be the perceiver of objects like sound etc. presented by the intellect etc., in this very way, the Self, which in reality is immutable, is said to be the ‘knower’ because of Its association with the knowledge of the distinction between the Self and non-Self, which (knowledge) is a modification of the intellect [By buddhi-vrtti, modification of the intellect, is meant the transformation of the internal organ into the form of an extension upto an object, along with its past impressions, the senses concerned, etc., like the extension of the light of a lamp illuminating an object. Consciousness reflected on this transformation and remaining indistinguishable from that transformation revealing the object, is called objective knowledge. Thereby, due to ignorance, the Self is imagined to be the perceiver because of Its connection with the vrtti, modification. (-A.G.) The process is elsewhere described as follows: The vrtti goes out through the sense-organ concerned, like the flash of a torchlight, and along with it goes the reflection of Consciousness. Both of them envelop the object, a pot for instance. The vrtti destroys the ignorance about the pot; and the reflection of Consciousness, becoming unified with only that portion of it which has been delimited by the pot, reveals the pot. In the case of knowledge of Brahman, it is admitted that the vrtti in the form, ‘I am Brahman’, does reach Brahman and destroys ignorance about Brahman, but it is not admitted that Brahman is revealed like a ‘pot’, for Brahman is self-effulgent.-Tr.] and is unreal by nature. From the statement that action is impossible for man of realization it is understood that the conclusion of the Lord is that, actions enjoined by the scriptures are prescribed for the unenlightened. Objection: Is not elightenment too enjoined for the ignorant? For, the injunction about enlightenment to one who has already achieved realization is useless, like grinding something that has already been ground! This being so, the distinction that rites and duties are enjoined for the unenlightened, and not for the enlightened one, does not stand to reason. Vedantin: No. There can reasonable be a distinction between the existence or nonexistence of a thing to be performed. As after the knowledge of the meaning of the injunction for rites like Agnihotra etc. their performance becomes bligatory on the unenlightened one who thinks, ‘Agnihotra etc. has to be performed by collecting various accessories; I am the agent, and this is my duty’, — unlike this, nothing remains later on to be performed as a duty after knowing the meaning of the injunction about the nature of the Self from such texts as, ‘Never is this One born,’ etc. But apart from the rise of knowledge regarding the unity of the Self, his non-agency, etc., in the form, ‘I am not the agent, I am not the enjoyer’, etc., no other idea arises. Thus, this distinction can be maintained. Again, for anyone who knows himself as, ‘I am the agent’, there will necessarily arise the idea, ‘This is my duty.’ In relation to that he becomes eligible. In this way duties are (enjoined) [Ast. adds ‘sambhavanti, become possible’.-Tr.] for him. And according to the text, ‘both of them do not know’ (19), he is an unenlightened man. And the text, ‘How can that person,’ etc. concerns the enlightened person distinguished above, becuase of the negation of action (in this text). Therefore, the enlightened person distinguished above, who has realized the immutable Self, and the seeker of Liberation are qualified only for renunciation of all rites and duties. Therefore, indeed, the Lord Narayana, making a distinction between the enlightened man of Knowledge and the unenlightened man of rites and duties, makes them take up the two kinds of adherences in the text, ‘through the Yoga of Knowledge for the men of realization; through the Yoga of Action for the yogis’ (3.3). Similarly also, Vyasa said to his son, ‘Now, there are these two paths,’ etc. [‘Now, there are these two paths on which the Vedas are based. They are thought of as the dharma characterized by engagement in duties, and that by renunciation of them’ (Mbh. Sa. 241.6).-Tr.] So also (there is a Vedic text meaning): ‘The path of rites and duties, indeed, is the earlier, and renunciation comes after that.’ [Ast. says that this is not a quotation, but only gives the purport of Tai, Ar. 10.62.12.-Tr.] The Lord will show again and again this very division: ‘The unenlightened man who is deluded by egoism thinks thus: “I am the doer”; but the one who is a knower of the facts (about the varieties of the gunas) thinks, “I do not act”‘ (cf. 3.27,28). So also there is the text, ‘(The embodied man of selfcontrol,) having given up all actions mentally, continues (happily in the town of nine gates)’ (5.13) etc. With regard to this some wiseacres say: In no person does arise the idea, ‘I am the changeless, actionless Self, which is One and devoid of the six kinds of changes beginning with birth to which all things are subject’, on the occurrence of which (idea alone) can renunciation of all actions be enjoined. That is not correct, because it will lead to the needlessness of such scriptural instructions as, ‘Never is this One born,’ etc. (20). They should be asked: As on the authority of scripural instructions there arises the knowledge of the existence of virtue and vice and the knowledge regarding an agent who gets associated with successive bodies, similarly, why should not there arise from the scriptures the knowledge of unchangeability, non-agentship, oneness, etc. of that very Self? Objection: If it be said that this is due to Its being beyond the scope of any means (of knowledge)? Vedantin: No, because the Sruti says, ‘It is to be realized through the mind alone, (following the instruction of the teacher)’ (Br. 4.4.19). The mind that is purified by the instructions of the scriptures and the teacher, control of the body and organs, etc. becomes the instrument for realizing the Self. Again, since there exist inference and scriptures for Its realization, it is mere bravado to say that Knowledge does not arise. And it has to be granted that when knowledge arises, it surely eliminates ignorance, its opposite. And that ignorance has been shown in, ‘I am the killer’, ‘I am killed’, and ‘both of them do not know’ (see 2.19). And here also it is shown that the idea of the Self being an agent, the object of an action, or an indirect agent, is the result of ignorance. Also, the Self being changeless, the fact that such agentship etc. are cuased by ignorance is a common factor in all actions without exception, because only that agent who is subject to change instigates someone else who is different from himself and can be acted on, saying, ‘Do this.’ Thus, with a view to pointing out the absence of fitness for rites and duties in the case of an enlightened person, the Lord [Ast, adds vasudeva after ‘Lord’.-Tr.] says, ‘He who knows this One as indestructible,’ ‘how can that person,’ etc. — thereby denying this direct and indirect agentship of an enlightened person in respect of all actions without exception. As regards the question, ‘For what, again, is the man of enlightenment qualified?’, the answer has already been give earlier in, ‘through the Yoga of Knowledge for the men of realization’ (3.3). Similarly, the Lord will also speak of renunication of all actions in, ‘having given up all actions mentally,’ etc.(5.13). Objection: May it not be argued that from the expression, ‘mentally’, (it follows that) oral and bodily actions are not to be renounced? Vedantin: No, because of the categoric expression, ‘all actions’. Objection: May it not be argued that ‘all actions’ relates only to those of the mind? Vedantin: No, because all oral and bodily actions are preceded by those of the mind, for those actions are impossible in the absence of mental activity. Objection: May it not be said that one has to mentally renounce all other activities except the mental functions which are the causes of scriptural rites and duties performed through speech and body? Vedantin: No, because it has been specifically expressed: ‘without doing or causing (others) to do anything at all’ (5.13). Objection: May it not be that this renunciation of all actions, as stated by the Lord, is with regard to a dying man, not one living? Vedantin: No, because (in that case) the specific statement, ‘The embodied man…continues happily in the town of nine gates’ (ibid.) will become illogical since it is not possible for a dead person, who neither acts nor makes others act, [The words ‘akurvatah akarayatah, (of him) who neither acts nor makes others act’, have been taken as a part of the Commentator’s arguement. But A.G. points out that they can also form a part of the next Objection. In that, case, the translation of the Objection will be this: Can it not be that the construction of the sentence (under discussion) is — Neither doing nor making others do, he rest by depositing (sannyasya, by renouncing) in the body’, but not ‘he rests in the body by renouncing…’?] to rest in that body after renouncing all actions. Objection: Can it not be that the construction of the sentence (under discussion) is, ‘(he rests) by depositing (sannyasya, by renouncing) in the body’, (but) not ‘he rests in the body by renouncing…’? Vedantin: No, because everywhere it is categorically asserted that the Self is changeless. Besides, the action of ‘resting’ requires a location, whereas renunciation is independent of this. The word nyasa preceded by sam here means ‘renunciation’, not ‘depositing’. Therefore, according to this Scripture, viz the Gita, the man of realization is eligible for renunciation, alone, not for rites and duties. This we shall show in the relevant texts later on in the cotext of the knowledge of the Self. And now we shall speak of the matter on hand: As to that, the indestructibility [Indestructibility suggests unchangeability as well.] of the Self, has been postulated. What is it like? That is being said in, ‘As after rejecting wornout clothes,’ etc.
Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:    

2.21 Veda etc. Whosoever, because of his realisation, under-stands this Self as ‘This neither slays [any one]. nor is This slain [by any one] – how could there be any bondage for him ?
Sanskrit Shloka Without Transliteration Marks:

vedavinasinam nityam
ya enam ajam avyayam
katham sa purusah partha
kam ghatayati hanti kam
Sanskrit to English Word for Word Meanings:

veda — knows; avināśinam — indestructible; nityam — always existing; yaḥ — one who; enam — this (soul); ajam — unborn; avyayam — immutable; katham — how; saḥ — that; puruṣaḥ — person; pārtha — O Pārtha (Arjuna); kam — whom; ghātayati — causes to hurt; hanti — kills; kam — whom.