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 $\displaystyle <A,O>$ be a system with identity $\displaystyle e$ in which $\displaystyle O$ is associative. If $\displaystyle b$ is a left-inverse for $\displaystyle a \in A$ and c a right-inverse for a, then b = c. As corollaries, show that (a) a two inverse is unique, and (b) if $\displaystyle O$ is commutative, then $\displaystyle <A,O>$ 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.