If A=⎡⎢⎣111111111⎤⎥⎦, prove that An=⎡⎢⎣3n−13n−13 – InterviewSolution

1.	If A=⎡⎢⎣111111111⎤⎥⎦, prove that An=⎡⎢⎣3n−13n−13n−13n−13n−13n−13n−13n−13n−1⎤⎥⎦,n∈N.
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ , prove that $A^{n} = ⎡ ⎢ ⎣ \begin{matrix} 3^{n - 1} & 3^{n - 1} & 3^{n - 1} 3^{n - 1} & 3^{n - 1} & 3^{n - 1} 3^{n - 1} & 3^{n - 1} & 3^{n - 1} \end{matrix} ⎤ ⎥ ⎦, n \in N$ .

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