Proof: Invertibility implies a unique solution to f(x)=y | Linear Algebra | Khan Academy

Proof: Invertibility implies a unique solution to f(x)=y for all y in co-domain of f.

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[alkalait]

I can spot an analogy, although oversimplistic, of the identity (or 1 in the univariate case) with the wave state of a particle in quantum mechanics.
Both entities have the potential of an infinite variability of instantiations. The identity to an infinite set of f/f-inverse compositions, and the particle to a set of infinite possible trajectories.
Even more, both entities revert to some state under observation. The particle wave collapses to a value; the f-inverse is defined under an assumed f.

[jamesmaxwell]

I think the video should have stopped at 8:14. Everything after that is repetitive and cofusing. Or maybe I missed something.

[c]

What grade is this taught? I'm trying to get ahead because im going to high school this year and COVID has made me lose some of my education. I want to be able to have some base knowledge for the next school year. Is this taught in the 9th or above?