If A and B are idempotent(A=A^2) and AB=BA, prove that AB is idempotent. this is what i got so far. AB=BA AB=B^(2)A^(2) AB=(BA)^(2) this is where I get stuck. Do A and B have inverses? if so, why? should I be thinking about inverses or is there another way of approaching this problem?
i doubt you can switch those matrices b/c youre multiplying the two of them. This has got be wrong. there has to be a different way to get what im trying to get.
As has been pointed out THEY COMMUTE! But that isn't why I post. I want to point out that only in the trivial case can an idempotent be invertible.
so if i start the proof off with AB=BA then I can use AB=BA later on in the proof I started off with in the firszt place?