Singular Matrix

If the determinant of a square matrix $A$ is equal to zero, then we say that $A$ is a singular matrix.

If a matrix is singular, then it does not have a multiplicative inverse.

For example, consider the inverse of a 2x2 matrix, for which we have:

$$A^{-1}=\frac{1}{\det (A)}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$$

If $\det (A)=0$, then $A^{-1}$ wouldn’t exist