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  4. If A = beginpmatrix0&0&1 0&1&0 1&0&0 endpmatrix, then A4 is equal to

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Q. If $A = \begin{pmatrix}0&0&1\\ 0&1&0\\ 1&0&0\end{pmatrix}$, then $A^4$ is equal to

KCETKCET 2020

Solution:

$A^{2}=\begin{pmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{pmatrix}\begin{pmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{pmatrix}=I$
$\therefore A^{4}=\left(A^{2}\right)^{2}=I^{2}=I$