Let S be a ring such that for all s in S, s2 = s. Prove that S is commutative. I've proved that for all s and t in S, (s + t)2 = s2 + t2, and also that s + s = 0. How would I go about proving that for all s and t, st = ts? Thanks. By the way, this isn't exactly homework, I was just practicing for the GREs.