Answer
$A^{-1}=\left[\begin{array}{ll}
-5/3 & -4/3\\
-8/3 & -7/3
\end{array}\right]$
Work Step by Step
$A=\displaystyle \left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right] \Rightarrow A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ll}
d & -b\\
-c & a
\end{array}\right]$
($A^{-1}$ exists if and only if $ad-bc\neq 0)$
----
$\left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right]=\left[\begin{array}{ll}
-7 & 4\\
8 & -5
\end{array}\right]$
$ad-bc=-7(-5)-(4)(8)=3\neq 0$
$A^{-1}=\displaystyle \frac{1}{3}\cdot\left[\begin{array}{ll}
-5 & -4\\
-8 & -7
\end{array}\right]$
$A^{-1}=\left[\begin{array}{ll}
-5/3 & -4/3\\
-8/3 & -7/3
\end{array}\right]$
