Answer
The matrix does not have an inverse.
Work Step by Step
Consider the given matrix $ A=\left[ \begin{matrix}
6 & -3 \\
-2 & 1 \\
\end{matrix} \right]$
Now, by using the inverse formula we get:
${{A}^{-1}}=\frac{1}{\left| ad-bc \right|}\left[ \begin{matrix}
d & -b \\
-c & a \\
\end{matrix} \right]$
Let, $\begin{align}
& a=6 \\
& b=-3 \\
& c=-2 \\
& d=1
\end{align}$
Substitute the values to get
$\begin{align}
& {{A}^{-1}}=\frac{1}{\left| ad-bc \right|}\left[ \begin{matrix}
d & -b \\
-c & a \\
\end{matrix} \right] \\
& {{A}^{-1}}=\frac{1}{\left| 6\times 1-\left( -3 \right)\times \left( -2 \right) \right|}\left[ \begin{matrix}
1 & 3 \\
2 & 6 \\
\end{matrix} \right] \\
& =\frac{1}{0}\left[ \begin{matrix}
2 & -3 \\
1 & 2 \\
\end{matrix} \right]
\end{align}$
So, therefore the matrix does not have an inverse
$ ab-bc=0$
