Module on Cartesian Product of Ring with Unity is Unitary Module/Proof 1
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Theorem
Let $\struct {R, +_R, \times_R}$ be a ring with unity.
Let $n \in \N_{>0}$.
Let $\struct {R^n, +, \times}_R$ be the $R$-module $R^n$.
Then $\struct {R^n, +, \times}_R$ is a unitary $R$-module.
Proof
This is a special case of Direct Product of Unitary Modules is Unitary Module.
$\blacksquare$