so I have $A - B + A^2 - AB = I$. I'm afraid I'm stuck now, how can I prove that $A-B$ has an inverse?
2026-04-24 14:35:15.1777041315
Linear algebra proof that there is an inverse
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You can factor your expression like this:
$$ (A-B)+A(A-B) = I\implies (I+A)(A-B)= I$$
So $I+A$ is inverse for $A-B$.