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## Homework Statement

Let A, B be both matrices with the same dimensions. Is AB^2 = (A^2)(B^2) a valid claim?

## Homework Equations

## The Attempt at a Solution

I attempted to show that (AB)^2 = (AB)(AB) = A(BA)B

and that (A^2)(B^2) = (AA)(BB) = A(AB)B, so for A(BA)B to be equal to A(AB)B, AB must be equal to BA, which is not always true.

I discarded this approach as nothing assures me that A and B are both invertible, and thus I cannot prove that A(BA)B = A(AB)B implies BA = AB. My teacher is kinda picky about this stuff.

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