Definition:Non-Invertible Matrix/Definition 1

Definition
Let $\left({R, +, \circ}\right)$ be a ring with unity.

Let $\mathcal M_R \left({n}\right)$ be the $n \times n$ matrix space over $R$.

Let $\mathbf A$ be an element of the ring $\left({\mathcal M_R \left({n}\right), +, \times}\right)$.

Let $\mathbf A$ have no inverse.

Then $\mathbf A$ is referred to as non-invertible.

Also see

 * Equivalence of Definitions of Non-Invertible Matrix