Interesting! read the verse translation – it seems as if it was lifted off from Gita! Gita is a treatise on Vedas and Upanishads. Krishna does not just come up with stuff on his own. He clarifies it for the people. And that is Gita’s strength!
The all-knowing Self was never born,
Nor will it die. Beyond cause and effect,
This Self is eternal and immutable.
When the body dies, the Self does not die.
If the slayer believes that he can slay
Or the slain believes that he can be slain,
Neither knows the truth. The eternal Self
Slays not, nor is ever slain.