If $A$ and $B$ are square matrices of size $n\, \times \,n$ such that ${A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right),$ then which of the following will be always true?

Question

If $A$ and $B$ are square matrices of size $n\, \times \,n$ such that
${A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right),$ then which of the following will be always true?

$A=B$

$AB=BA$

either of $A$ or $B$ is a zero matrix

either of $A$ or $B$ is identity matrix

Solution

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