Associativity of Operation in Group Direct Product/Proof 1

Theorem
Let $\left({G \times H, \circ}\right)$ be the group direct product of the two groups $\left({G, \circ_1}\right)$ and $\left({H, \circ_2}\right)$.

Then the operation $\circ$ in $\left({G \times T, \circ}\right)$ is associative.

Proof
Thus $\circ$ is seen to be associative in $\left({G \times H, \circ}\right)$.