Answer:
Observe that
[tex](A+B)(A-B)=AA-AB+BA-BB=A^2-AB+BA-B^2[/tex]
Since the product of matrices isn't commutative, then for any matrices A and B [tex]A\neq B[/tex].
Then, if we want that [tex](A+B)(A-B)=A^2-B^2[/tex], we need impose the condition that [tex]AB=BA[/tex]
