If `A=[(1 ,2 ),(2, 1)]` and `f(x)=x^2-2x-3` , show that `f(A)=O` .

Explanation

To show that \( f(A) = O \) where \( A = \begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix} \) and \( f(x) = x^2 - 2x - 3 \), we will follow these steps:

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

First, we need to calculate \( A^2 \):

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