Prove True or false : If $A$ and $B$ are $n\times n$ invertible matrices and $(AB)^2=A^2B^2$, then $AB=BA$.
This looks like it is false, but the thing is I can't find a counter example for it.
2026-04-17 22:40:06.1776465606
Prove True or false : If $A$ and $B$ are nxn invertible matrices and $(AB)^2=A^2B^2$, then $AB=BA$
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HINT: Multiply $(AB)^2=A^2B^2$ on the left by $A^{-1}$ and on the right by ...