If `A=[(a,b),(c,d)]`, where a, b, c and d are real numbers, then prove that `A^(2)-(a+d)A+(ad-bc) I=O`. Hence or therwise, prove that if `A^(3)=O` then `A^(2)=O`

Explanation

To prove the statement \( A^2 - (a+d)A + (ad - bc)I = O \) for the matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), 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} a & b \\ c & d \end{pmatrix} \cdot \begin{pmatrix} a & b \\ c & d \end{pmatrix}
...