If `A=((p,q),(0,1))`, then show that `A^(8)=((p^(8),q((p^(8)-1)/(p-1))),(0,1))`

Explanation

To show that \( A^8 = \begin{pmatrix} p^8 & q \frac{p^8 - 1}{p - 1} \\ 0 & 1 \end{pmatrix} \) for the matrix \( A = \begin{pmatrix} p & q \\ 0 & 1 \end{pmatrix} \), we will calculate powers of \( A \) step by step.

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

We start with:
\[ A = \begin{pmatrix} p & q \\ 0 & 1 \end{pmatrix} \]
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