If `A=[(1,a),(0, 1)]` , then `A^n` (where `n in N)` equals `[(1,n a),(0, 1)]` (b) `[(1,n^2a),(0, 1)]` (c) `[(1,n a),(0 ,0)]` (d) `[(n,n a),(0,n)]`

Explanation

To solve the problem, we need to find the expression for \( A^n \) where \( A = \begin{pmatrix} 1 & a \\ 0 & 1 \end{pmatrix} \) and \( n \) is a natural number. We will use the method of induction to derive the formula for \( A^n \).

### Step-by-Step Solution:

**Step 1: Base Case (n = 1)**

For \( n = 1 \):
\[
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