Show that thematrix A=`[{:(,2,3),(,1,2):}]` satisfies the equations `A^(2)-4A+I=0` where I is `2 xx 2` identity matrix and O is `2 xx 2` zero matrix. Using the equations. Find `A^(-1)`.

Explanation

To show that the matrix \( A = \begin{pmatrix} 2 & 3 \\ 1 & 2 \end{pmatrix} \) satisfies the equation \( A^2 - 4A + I = 0 \), where \( I \) is the \( 2 \times 2 \) identity matrix, and to find \( A^{-1} \), we will follow these steps:

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

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

\[
A^2 = A \cdot A = \begin{pmatrix} 2 & 3 \\ 1 & 2 \end{pmatrix} \cdot \begin{pmatrix} 2 & 3 \\ 1 & 2 \end{pmatrix}
...