\begin{definition}[Definition:Ring of Square Matrices]
Let $R$ be a ring.
Let $n \in \Z_{>0}$ be a (strictly) positive integer.
Let $\map {\MM_R} n$ denote the $n \times n$ matrix space over $R$.
Let $+$ denote the operation of matrix entrywise addition.
Let $\times$ be (temporarily) used to denote the operation of conventional matrix multiplication. 
The algebraic structure:
:$\struct {\map {\MM_R} n, +, \times}$
is known as the '''ring of square matrices of order $n$ over $R$'''
\end{definition}