What is a singular matrix?

Singular matrix: A square matrix is singular if and only if the value of its determinant is zero.

The inverse of a singular matrix does not exist.

Example: $A=\left[\begin{array}{cc}2& 1\\ 6& 3\end{array}\right]$

The determinant of the matrix is,

$\left|A\right|=2·3-6·1$

$\Rightarrow$ $\left|A\right|=6-6$

$\Rightarrow$ $\left|A\right|=0$

Hence, the matrix $A$ is a singular matrix.