Question

Find the inverse of the matrices , if it exists.
$\left[\begin{array}{cc}6& -3\\ -2& 1\end{array}\right]$

Answer 1

Let $A=\left[\begin{array}{cc}6& -3\\ -2& 1\end{array}\right]$
$|A|=6\left(1\right)-(-3)(-2)=6-6=0$

$\Rightarrow A$ is singular matrix.
Therefore, $A^{-1}$ does not exist.