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If $ A=\begin{bmatrix} 1& 1 & 1 \\ 1& 1 & 1 \\ 1& 1 & 1 \end{bmatrix}$ then prove that $ A^n=\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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