If A and B are square matrices of size n n such that A^2-B^2=(A-B)(A+B), then which of the…

Question

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

Accepted Answer

$${A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right)$$

${A^2} - {B^2} = {A^2} + AB - BA - {B^2}$

$$ \Rightarrow AB = BA$$

Solutions · 1