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Multiplication of Matrices

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Question

Say true or false:
If $A$ , $B$ be two matrices such that they commute, then $A^{2} - B^{2} = (A - B) (A + B)$ .

A

True

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B

False

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Solution

The correct option is A True
$A$ and $B$ commute when $A B = B A$
Hence $(A - B) (A + B) = A^{2} + A B - B A - B^{2} = A^{2} - B^{2}$

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