Let G be a set together with a binary operation. Suppose that this operation is associative, there exist an element e in G such that ae = a for each a in G, for each a in G, there is an element b in G such that ab = e.

Prove G is a group.

My Proof so far:

Now, I understand that I need to show ea = a and ba = e.

Is it proper for me to assume be = b? Or rather, would this help?