External Direct Product Commutativity

Theorem
Let $\left({S \times T, \circ}\right)$ be the external direct product of the two algebraic structures $\left({S, \circ_1}\right)$ and $\left({T, \circ_2}\right)$.

If $\left({S, \circ_1}\right)$ and $\left({T, \circ_2}\right)$ are commutative, then $\left({S \times T, \circ}\right)$ is also commutative.

Proof
Let $\left({S, \circ_1}\right)$ and $\left({T, \circ_2}\right)$ be commutative.

and we see that $\left({S \times T, \circ}\right)$ is commutative.