The value of the determinant of the matrix (S -2) is 7. a) Find the value of x b) Hence write down the inverse of the matrix -4 x

For a matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$, the determinant is $ad - bc$.

The matrix is now $A = \begin{pmatrix} 5 & -2 \\ -4 & 3 \end{pmatrix}$.
The determinant is given as 7.

For a matrix $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$, the inverse is $A^{-1} = \frac{1}{\det(A)} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$.

Here, $a=5$, $b=-2$, $c=-4$, $d=3$, and $\det(A)=7$.