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14.If \( A=\left[\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right] \), find \( A^{2} \).Hence find \( A^{6} \) |
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Answer» \(A=\left[\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right]\) \(A = 0\begin{bmatrix}1&0\\0&0\end{bmatrix} - 0\begin{bmatrix}0&0\\1&0\end{bmatrix} + 1\begin{bmatrix}0&1\\1&0\end{bmatrix}\) \(A= 0(1 - 0) - 0(0 - 1) + 1(0 - 1)\) \(A = -1\) \(⇒ A^2 = 1\) \(⇒ A^6 = 1\) |
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