Question

Find each matrix A, find the inverse matrix, A^1, or identify A as a singular matrix

Answer 1

$\begin{pmatrix} a & b \\ c & d \end{pmatrix}^{-1} = \dfrac{1}{ad-bc} \begin{pmatrix}{ d & -b \\ -c & a}\end{pmatrix}$

$\begin{pmatrix} 5 & 7 \\ 2 & 3 \end{pmatrix}^{-1} = \dfrac{1}{5(3)-2(7)}\begin{pmatrix} 3 & -7 \\ -2 & 5 \end{pmatrix}$

Answer: $\begin{pmatrix} 3 & -7 \\ -2 & 5 \end{pmatrix}$