\begin{definition}[Definition:Non-Invertible Matrix/Definition 2]
Let $\struct {R, +, \circ}$ be a ring with unity.
Let $n \in \Z_{>0}$ be a (strictly) positive integer.
Let $\mathbf A$ be an element of the ring of square matrices $\struct {\map {\MM_R} n, +, \times}$.
Let the determinant of $\mathbf A$ be equal to $0$.
Then $\mathbf A$ is referred to as '''non-invertible'''.
\end{definition}