The self does not kill, nor is it killed. For the self is never born and never dies, nor may it ever become non-existent. This unborn, everlasting, abiding self is not slain when the body is slain. Knowing the self to be unborn, imperishable, everlasting, changeless, Arjuna, how can a man slay anyone or be slain?
As a man gets rid of worn out clothes and puts on new ones, so the self puts away worn-out bodies and puts on others that are new. Weapons do not cut up the self, fire does not burn it, water does not wet it, the wind does not dry it. Not capable of being cut, burned, wet, or dried, the self is everlasting, present in all things, unchangeable, unmoveable, for ever the same.
Knowing that the soul is immaterial and unalterable, you should not grieve, Arjuna.