Suppose that A and B are square matrices of order n. For each statement:
(a) (A-B)^2 = A^2 - 2AB + B^2
(b) (A+B)(A-B) = (A-B)(A+B)
(c) (A+B)^2 - (A-B)^2 = 2(AB +BA)
either prove the equation is always true or give an example to show that it is false. If the equation is false, can you fund an condition which would make it generally true?