If `A=[(1 ,1),( 0, 1)]` , prove that `A^n=[(1,n),(0, 1)]` for all positive integers `ndot`

Explanation

To prove that \( A^n = \begin{pmatrix} 1 & n \\ 0 & 1 \end{pmatrix} \) for all positive integers \( n \), we will use the principle of mathematical induction.

### Step 1: Base Case
We start with the base case where \( n = 1 \).

\[ A^1 = A = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix} \]
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