Null Ring is Commutative Ring

Theorem
Let $R$ be the null ring.

That is, let:
 * $R := \struct {\set {0_R}, +, \circ}$

where ring addition and ring product are defined as:


 * $0_R + 0_R = 0_R$
 * $0_R \circ 0_R = 0_R$

Then $R$ is a commutative ring.

Proof
From Null Ring is Trivial Ring, we have that $R$ is a trivial ring.

The result follows from Trivial Ring is Commutative Ring.