Answer
$\begin{bmatrix} -3 &2 \\ -2 & 1\end{bmatrix}$
Work Step by Step
$A=\begin{bmatrix} 1 & -2 \\ 2 & -3\end{bmatrix}$
Therefore, the general form of a matrix of order $ 2 \times 2$ is:
$\begin{bmatrix} p & q \\ r & s\end{bmatrix}=ps-qr$
Now, $ps-qr=\begin{bmatrix} 1 & -2 \\ 2 & -3\end{bmatrix}=-3+4=1 \ne 0$
$A^{-1}=\dfrac{1}{1} \begin{bmatrix} -3 & 2 \\ -2 & -1 \end{bmatrix}$
Our answer is: $\begin{bmatrix} -3 &2 \\ -2 & 1\end{bmatrix}$
