Answer
$A^{-1}=\left[\begin{array}{ll}
2/7 & -3/7\\
1/7 & 2/7
\end{array}\right]$
Work Step by Step
$ad-bc=4-(-3)=7$
$A^{-1}=\displaystyle \frac{1}{7}\left[\begin{array}{ll}
2 & -3\\
1 & 2
\end{array}\right]=\displaystyle \left[\begin{array}{ll}
2/7 & -3/7\\
1/7 & 2/7
\end{array}\right]$
Check:
$AA^{-1}=\left[\begin{array}{ll}
2(\frac{2}{7})+3(\frac{1}{7}) & 2(-\frac{3}{7})+3(\frac{2}{7})\\
-1(\frac{2}{7})+2(\frac{1}{7}) & -1(-\frac{3}{7})+2(\frac{2}{7})
\end{array}\right]=\left[\begin{array}{ll}
7/7 & 0\\
0 & 7/7
\end{array}\right]=I_{2}$
$A^{-1}A=\left[\begin{array}{ll}
\frac{2}{7}(2)+(-\frac{3}{7})(-1) & \frac{2}{7}(3)+(-\frac{3}{7})(2)\\
\frac{1}{7}(2)+(\frac{2}{7})(-1) & \frac{1}{7}(3)+(\frac{2}{7})(2)
\end{array}\right]=\left[\begin{array}{ll}
7/7 & 0\\
0 & 7/7
\end{array}\right]=I_{2}$
