Boolean rings are commutative of characteristic 2

Let \(R\) be a ring, possibly noncommutative and possibly without an identity, in which every element is idempotent: \(a^2=a\) for all \(a\in R\). Show that \(R\) has characteristic \(2\) (that is, \(2a=0\) for all \(a\)) and is commutative.