Answer
$\begin{bmatrix}3&1\\2&1\end{bmatrix}$
Work Step by Step
We are given the matrix:
$A=\begin{bmatrix} 1&-1\\-2&3\end{bmatrix}$
In order to find its inverse $A^{-1}$, first we compute its determinant $D$:
$D=3(1)-(-1)(-2)=1$
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 $A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$
$A^{-1}=\dfrac{1}{1}\begin{bmatrix}3&1\\2&1\end{bmatrix}$
$=\begin{bmatrix}3&1\\2&1\end{bmatrix}$
