Recall that a group contains an element e such that ex = x = xe for every x in the group. Now assume that we are given some element a such that for one specific y we have ay = y. Show that a must be the identity of the group. note: This shows that the identity of a group is really really unique. If ay = y for just one element y then ax = xa = x for every element x. Any element that appears just for one moment to behave like it might be the identity in one circumstance, must be the identity. Despite the length of the question,the solution is possibly the shortest solution you will write.