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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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\(A=\left[\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right]\)

\(A = 0\begin{bmatrix}1&0\\0&0\end{bmatrix} - 0\begin{bmatrix}0&0\\1&0\end{bmatrix} + 1\begin{bmatrix}0&1\\1&0\end{bmatrix}\)

\(A= 0(1 - 0) - 0(0 - 1) + 1(0 - 1)\)

\(​​A = -1\)

\(⇒ A^2 = 1\)

\(⇒ A^6 = 1\)

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