Answer
$A^{-1}=\left[\begin{array}{rr}
1 & -2\\
-3/2 & 7/2
\end{array}\right]$
Work Step by Step
$A=\displaystyle \left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right] \Rightarrow A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ll}
d & -b\\
-c & a
\end{array}\right]$
----
$A^{-1}=\displaystyle \frac{1}{7(2)-4(3)}\left[\begin{array}{ll}
2 & -4\\
-3 & 7
\end{array}\right]$
$=\displaystyle \frac{1}{2}\left[\begin{array}{ll}
2 & -4\\
-3 & 7
\end{array}\right]$
$=\left[\begin{array}{ll}
1 & -2\\
-3/2 & 7/2
\end{array}\right]$
