Answer
\[{\text{The inverse does not exist}}\]
Work Step by Step
\[\begin{gathered}
\left[ {\begin{array}{*{20}{c}}
5&{10} \\
{ - 3}&{ - 6}
\end{array}} \right] \hfill \\
{\text{Let a matrix A}} = \left[ {\begin{array}{*{20}{c}}
a&b \\
c&d
\end{array}} \right],{\text{ its inverse is: }}{{\text{A}}^{ - 1}} = \frac{1}{{ad - bc}}\left[ {\begin{array}{*{20}{c}}
d&{ - b} \\
{ - c}&a
\end{array}} \right] \hfill \\
{\text{Then}} \hfill \\
{{\text{A}}^{ - 1}} = \frac{1}{{\left( 5 \right)\left( { - 6} \right) - \left( {10} \right)\left( { - 3} \right)}}\left[ {\begin{array}{*{20}{c}}
{ - 6}&{ - 10} \\
3&5
\end{array}} \right] \hfill \\
{\text{Simplifying}} \hfill \\
{{\text{A}}^{ - 1}} = \frac{1}{{ - 30 + 30}}\left[ {\begin{array}{*{20}{c}}
{ - 6}&{ - 10} \\
3&5
\end{array}} \right] \hfill \\
{{\text{A}}^{ - 1}} = \frac{1}{0}\left[ {\begin{array}{*{20}{c}}
{ - 6}&{ - 10} \\
3&5
\end{array}} \right] \hfill \\
{\text{The inverse does not exist}} \hfill \\
\end{gathered} \]
