Commutative Rings

Let R be a ring. Then prove the following:

1. If for all nonzero a ∈ R, a^2 = 1, then R is abelian (that is, for all a, b ∈ R, ab = ba).

2. If for all non-1 a ∈ R, a^2 = 0, then R is abelian.

3. If for all a ∈ R, a^2 = a, then R is abelian.