Answer
\[
M=1/2
\left[ {\begin{array}{cc}
4 & -3 \\
-2 & 2 \\
\end{array} } \right]
\]
\[
M=
\left[ {\begin{array}{cc}
2& -3/2 \\
-1& 1\\
\end{array} } \right]
\]
Work Step by Step
The inverse of a two by two matrix is swap of a and d and the negation of b and c, while multiplying the whole matrix by $1/(ad-bc)=1/2$
