I posted a thread not two long ago about one and two sided identities but I'm having a little confusion with inverses. The question is:

"Prove: Let be a system with identity in which is associative. If is a left-inverse for and c a right-inverse for a, then b = c. As corollaries, show that (a) a two inverse is unique, and (b) if is commutative, then has at most one left inverse."

I'm sure there is a super simple solution but it isn't immediately apparent to me, thanks in advance.