Answer
$\begin{bmatrix} \dfrac{1}{2}&-1\\-\dfrac{1}{6}&\dfrac{2}{3}\end{bmatrix}$
Work Step by Step
We are given the matrix:
$A=\begin{bmatrix}4&6\\1&3\end{bmatrix}$
In order to compute $A^{-1}$ use the formula:
$A^{-1}=\dfrac{1}{det A}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$
where
$A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$
and $det A=ad-bc$.
First compute $detA$:
$detA=4(3)-1(6)=6\not=0$
As $detA\not=0$, the inverse of $A$ exists. Determine $A^{-1}$:
$A^{-1}=\dfrac{1}{6}\begin{bmatrix} 3&-6\\-1&4\end{bmatrix}=\begin{bmatrix} \dfrac{1}{2}&-1\\-\dfrac{1}{6}&\dfrac{2}{3}\end{bmatrix}$
