Math Help - Group Proof

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?

Originally Posted by tttcomrader

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.

Maybe you are missing that b is unique?

I reread the problem and it doesn't say that b is unique. But I understand what you are saying, there can only exist one inverse of an element in a group.