Find the inverse of each of the matrices given below :
Show that the matrix `A=[(-8,5),(2,4)]` satisfies the equation `A^(2)+4A-42I=0` and hence find `A^(-1)`.

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} -8 & 5 \\ 2 & 4 \end{pmatrix} \) and show that it satisfies the equation \( A^2 + 4A - 42I = 0 \), we will follow these steps:

### Step 1: Calculate \( A^2 \)

To find \( A^2 \), we multiply matrix \( A \) by itself:

\[
A^2 = A \cdot A = \begin{pmatrix} -8 & 5 \\ 2 & 4 \end{pmatrix} \cdot \begin{pmatrix} -8 & 5 \\ 2 & 4 \end{pmatrix}
...