If `A=[(3, 1),( 1, 2)]`, show that `A^2-5A+5I=0`. Hence, find `A^(-1)`.

Explanation

To solve the problem, we need to show that \( A^2 - 5A + 5I = 0 \) for the matrix \( A = \begin{pmatrix} 3 & 1 \\ 1 & 2 \end{pmatrix} \) and then find the inverse of \( A \).

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

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

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