Hello, I need the answer to this question please.

1. (30 pts) For all the calculations and proofs you are required to do, state clearly the properties (if any) and laws (if any) used. Note that parts (a), (b), (c) and (d) are not related. (a) Given that A and B are square matrices, show that if AB = A and BA - B, then A and B are both idempotent