(C) Given $A = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$.First,we calculate $A^{2} = A \cdot A$:$A^{2} = \begin{bmatrix} 0 &

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(C) Given $A = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$.First,we calculate $A^{2} = A \cdot A$:$A^{2} = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix} \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} = I$.Now,we calculate $A^{4} = A^{2} \cdot A^{2}$:$A^{4} = I \cdot I = I$.Therefore,$A^{4} = I$.

Class 12 Mathematics 3-4. Matrices and Determinants Types of matrices, Algebra of matrices

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

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A
$A$
B
$2A$
C
$I$
D
$4A$

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

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