Suppose that * is a binary operation on a non-empty set S. Show that if (*,S) contains an identity e then e is unique.
Is this right?
e1 * x = x * e1 = x
x = e2
e1 * e2 = e2 * e1 = e2
then do for e2
e2 * x = x * e2 = x
x = e1
e2 * e1 = e1 * e2 = e1