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.