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Matrix Algebra and Multiplication Properties - Class XII
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If $A=\begin{bmatrix} 1 & 1 & 1 \ 1 & 1 & 1 \ 1 & 1 & 1 \end{bmatrix}$ then $A^n=\begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \ 3^{n-1} & 3^{n-1} & 3^{n-1} \ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix}$ , $n \in N$
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A
True
💡 Explanation:
For A = [[1,1,1],[1,1,1],[1,1,1]], A^2 = 3A, A^3 = 9A = 3^2 * A. By induction, A^n = 3^(n-1) * A. This matches the given matrix.