Bhagavad Gita 2.19

ya enaḿ vetti hantāraḿ
yaś cainaḿ manyate hatam
ubhau tau na vijānīto
nāyaḿ hanti na hanyate

Translation of Bhagavad Gita 2.19

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

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 Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

“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?Commentary by Sri Ramanuja of Sri Sampradaya:

2.19 With regard to “This” viz., the self, whose nature has been described above, he who thinks of It as the slayer, i.e., as the cause of slaying, and he who thinks ‘This’ (self) as slain by some cause or other — both of them do not know. As this self is eternal for the reasons mentioned above, no possible cause of destruction can slay It and for the same reason, It cannot be slain. Though the root ‘han’ (to slay) has the self for its object, it signifies causing the separation of the body from the self and not destruction of the self. Scriptural texts like ‘You shall not cause injury to beings’ and ‘The Brahmana shall not be killed’? (K. Sm. 8.2) indicate unsanctioned actions, causing separation of the body from the self. [In the above quotes, slaughter in an ethical sense is referred to, while the text refers to killing or separating the self from the body in a metaphsyical sense. This is made explicit in the following verse].
Commentary by Sri Sridhara Swami of Rudra Sampradaya:

Thus it can be clearly demonstrated that the grief that would arise due to the death of Bhishma and other exalted superiors has been negated. Also Arjunas statement in chapter one, verse thirty-five of not wanting to slay them has been proven equally groundless as well by the Supreme Lords explanation of the Ultimate Truth revealing that the eternal soul does not slay anything and the eternal soul cannot be slain by anything. The reason for this is given in the next verse.
Commentary by Sri Madhvacharya of Brahma Sampradaya:

In the minds of living entities identifying themselves only as their physical bodies, or as their species, planet, or country as the case may be; the declaration that one who thinks that one can be factually slain or one who thinks that one can factually slay are both deluded, poses bewilderment. What can be factually slain is the physical body but not the embodied soul. The living entity becomes alive only by the energising facility of the Supreme Lord by the activation of the soul. Thus the Supreme Lord is always to be worshipped and glorified.

Now begins the summation.

If the statement one who thinks the living entity is able to kill another living entity independently on their own would be considered then the statement of the Supreme Lord in chapter 11, verse 34 kill those whom have already been killed by Me would be contradictory. The word hantaram being applicable to the soul is applicable to the Supreme Lord as well.
Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

In this way after establishing the immortality of the soul, Lord Krishna informs Arjuna that for anyone to believe that it is possible for the soul to be slain or anyone believing that they can be responsible for the slaying of the soul, are both in complete ignorance. Not being able to fathom the intrinsic nature of the soul they cannot realize that the soul is never the instigator of any action nor is the soul ever the recepient of any action.
Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

2.19 But the ideas that you have, ‘Bhisma and others are neing killed by me in war; I am surely their killer’ — this idea of yours is false. How? Yah, he who; vetti, thinks; of enam, this One, the embodied One under consideration; as hantaram, the killer, the agent of the act of killing; ca, and; yah, he who, the other who; manyate, thinks; of enam, this One; as hatam, the killed — (who thinks) ‘When the body is killed, I am myself killed; I become the object of the act of killing’; ubhau tau, both of them; owing to non-discrimination, na, do not; vijanitah, know the Self which is the subject of the consciousness of ‘I’. The meaning is: On the killing of the body, he who thinks of the Self (– the content of the consciousness of ‘I’ –) [The Ast. omits this phrase from the precedig sentence and includes it in this place. The A.A. has this phrase in both the places.-Tr.] as ‘I am the killer’, and he who thinks, ‘I have been killed’, both of them are ignorant of the nature of the Self. For, ayam, this Self; owing to Its changelessness, na hanti, does not kill, does not become the agent of the act of killing; na hanyate, nor is It killed, i.e. It does not become the object (of the act of killing). The second verse is to show how the Self is changeless:
Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:    

2.19 Ya enam etc. Whosoever veiws This i.e., the Self and the body, to be the slayer and the slain, ignorance is in him. That is why he is in bondage. The same [point the Lord] clarifies –
Sanskrit Shloka Without Transliteration Marks:

ya enam vetti hantaram
yas cainam manyate hatam
ubhau tau na vijanito
nayam hanti na hanyate
Sanskrit to English Word for Word Meanings:

yaḥ — anyone who; enam — this; vetti — knows; hantāram — the killer; yaḥ — anyone who; ca — also; enam — this; manyate — thinks; hatam — killed; ubhau — both; tau — they; na — never; vijānītaḥ — are in knowledge; na — never; ayam — this; hanti — kills; na — nor; hanyate — is killed.