Say we have two square, non-singular matrices A and B, which are not equal to each other. And such that both AB and BA is defined. So will the only solutions to the equation AB = BA be that either one of them is the Identity matrix or A is the inverse of B or B is the inverse of A. But my teacher had said that the last two are true only when AB = BA = I (Identity matrix). But how can AB = BA be equal to something other than the Identity matrix ? Is it possible that : $$AB = BA \neq I$$
2026-04-24 19:20:03.1777058403
Can AB be anything other than the Identity matrix?
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any set of matrix that are simultaneously diagonalizable (meaning they have the same eigenvectors) verify your equality