Answer
$\begin{bmatrix}
-1&-\frac{1}{2}\\
-3&-2
\end{bmatrix}$
Work Step by Step
Using the formula,
$A^{-1} = \frac{1}{|A|}\times{Adj(A)}$
$where, A = \begin{bmatrix}-4&1\\6&-2\end{bmatrix}$
$Adj(A) = \begin{bmatrix}d&-b\\-c&a\end{bmatrix}, if A = \begin{bmatrix}a&b\\c&d\end{bmatrix}$
$\implies A^{-1} = \frac{1}{(-4)(-2)-(6)(1)}\times\begin{bmatrix}-2&-1\\-6&-4\end{bmatrix}$
$\quad=\frac{1}{2}\times\begin{bmatrix}-2&-1\\-6&-4\end{bmatrix} = \begin{bmatrix}
-1&-\frac{1}{2}\\
-3&-2
\end{bmatrix}$
