Q)
Let \( A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} \) , show that \( (aI + bA)^n = a^nI+na^{n-1}bA, \) where I is the identity matrix of order zero \( n \in N. \) If $ \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix} $ prove that : $ \begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix}, n \in N. $
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