Ring of Square Matrices over Ring with Unity

Theorem
Let $R$ be a ring with unity.

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $\struct {\map {\MM_R} n, +, \times}$ denote the ring of square matrices of order $n$ over $R$.

Then $\struct {\map {\MM_R} n, +, \times}$ is a ring with unity.

Proof
From Ring of Square Matrices over Ring is Ring we have that $\struct {\map {\MM_R} n, +, \times}$ is a ring.

As $R$ has a unity, the unit matrix can be formed.

The unity of $\struct {\map {\MM_R} n, +, \times}$ is this unit matrix.