Text 19

ya enam vetti hantaram
yas cainam manyate hatam
ubhau tau na vijanito
nayam hanti na hanyate

Translation

Neither he who thinks the living entity the slayer nor he who thinks it slain is in knowledge, for the self slays not nor is slain. 

Commentary by Srila Prabhupada

When an embodied living entity is hurt by fatal weapons, it is to be known that the living entity within the body is not killed. The spirit soul is so small that it is impossible to kill him by any material weapon, as will be evident from subsequent verses. Nor is the living entity killable, because of his spiritual constitution. What is killed, or is supposed to be killed, is the body only. This, however, does not at all encourage killing of the body. The Vedic injunction is ma himsyat sarva bhutani: never commit violence to anyone. Nor does understanding that the living entity is not killed encourage animal slaughter. Killing the body of anyone without authority is abominable and is punishable by the law of the state as well as by the law of the Lord. Arjuna, however, is being engaged in killing for the principle of religion, and not whimsically.

Commentary by Sri Visvanatha Cakravarti Thakur

"O friend Arjuna! You, a soul as well, are neither the performer of killing nor the object of killing." That is expressed in this verse.

He who thinks the jiva (enam) is the killer, that Arjuna is the killer of Bhisma and others, and he who thinks that the jiva is killed, that Arjuna is killed by Bhisma, are both ignorant. Therefore, what is your fear of infamy from the words of ignorant people who say that Arjuna killed his guru?