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If $A$ and $B$ are square matrices of size $n \times n$ such that $A^2-B^2=(A-B)(A+B)$, then which of the following will be always true?
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Verified Answer
The correct answer is:
AB = BA
AB = BA
$A^2-B^2=(A-B)(A+B)$
$A^2-B^2=A^2+A B-B A-B^2$
$\Rightarrow A B=B A$
$A^2-B^2=A^2+A B-B A-B^2$
$\Rightarrow A B=B A$
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