If `A=[[3, 1],[-1, 2]]`, show that `A^2-5A+7I=0`

Explanation

To show that \( A^2 - 5A + 7I = 0 \) for the matrix \( A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} \), we will follow these steps:

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

First, we need to find \( A^2 \) by multiplying matrix \( A \) with itself:

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