Answer
$A^{-1}=\left[\begin{array}{ll}
-1 & 3\\
-1/2 & 1
\end{array}\right]$
Work Step by Step
$ad-bc=-4-(-6)= 2$
$A^{-1}=\displaystyle \frac{1}{2}\left[\begin{array}{ll}
-2 & 6\\
-1 & 2
\end{array}\right]=\displaystyle \left[\begin{array}{ll}
-1 & 3\\
-1/2 & 1
\end{array}\right]$
Checking:
$AA^{-1}=\left[\begin{array}{ll}
2(-1)-6(-\frac{1}{2}) & 2(3)-6(1)\\
-1(-1)+2(-\frac{1}{2}) & -1(3)+2(1)
\end{array}\right]=\left[\begin{array}{ll}
1 & 0\\
0 & 1
\end{array}\right]$
$A^{-1}A=\left[\begin{array}{ll}
-1(2)+3(1) & -1(-6)+3(-2)\\
-\frac{1}{2}(2)+1(1) & -\frac{1}{2}(-6)+1(-2)
\end{array}\right]=\left[\begin{array}{ll}
1 & 0\\
0 & 1
\end{array}\right]$
