1. The problem statement, all variables and given/known data Let G be a set with an operation * such that: 1. G is closed under *. 2. * is associative. 3. There exists an element e in G such that e*x = x. 4. Given x in G, there exists a y in G such that y*x = e. Prove that G is a group. 2. Relevant equations I need to prove that x*e = x and x*y = e, with x, y, e as given above. 3. The attempt at a solution I dunno, I'm stumped. I've tried finding some sort of clever identity without any success.