Let `A=[(2,1),(0,3)]` be a matrix. If `A^(10)=[(a,b),(c,d)]` then prove that `a+d` is divisible by 13.

Explanation

To solve the problem, we need to find \( A^{10} \) for the matrix \( A = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix} \) and prove that \( a + d \) is divisible by 13, where \( A^{10} = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \).

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

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

\[
A^2 = A \cdot A = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix} \cdot \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix}
...