Let `A=[[0, 1],[ 0, 0]]`show that `(a I+b A)^n=a^n I+n a^(n-1)b A`, where I is the identity matrix of order 2 and `n in N`.

Explanation

To prove that \((aI + bA)^n = a^n I + n a^{n-1} b A\) for the given matrix \(A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\), we will use mathematical induction.

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

For \(n = 1\):
\[ (aI + bA)^1 = aI + bA \]
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