A ring R such that a 2 = a for all a R is called a

A ring R such that a² = a for all a ϵ R is called a Boolean ring. Prove that every Boolean ring R is commutative and a + a = 0 for all a ϵ R. [For an example of a Boolean ring, see Exercise l(b).]

Data from Exercise 1(b)

Let S be the set of all subsets of some fixed set U. For A,B ϵ S, define A + B = (A - B) U (B - A) and AB = A ∩ B. Then S is a ring. Is S commutative? Does it have an identity?