Answer
$\begin{bmatrix}\frac{3}{5}&-\frac{2}{5}\\\frac{1}{5}&\frac{1}{5}\end{bmatrix}$
Work Step by Step
$A=\begin{bmatrix} 1&2\\-1&3\end{bmatrix}$
In order to find its inverse $A^{-1}$, first we compute its determinant $D$:
$D=1(3)-2(-1)=5$
Because $D\not=0$, matrix $A$ has inverse. We use the formula:
$A^{-1}=\dfrac{1}{D}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$, where $A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$
$A^{-1}=\dfrac{1}{5}\begin{bmatrix}3&-2\\1&1\end{bmatrix}$
$=\begin{bmatrix}\frac{3}{5}&-\frac{2}{5}\\\frac{1}{5}&\frac{1}{5}\end{bmatrix}$
