Solution
= Solution
Using $A^3=I$, the matrix power reduces modulo three:
$$
\boxed{A^{3n+2}=A^2=\begin{pmatrix}0&0&1\\1&0&0\\0&1&0\end{pmatrix}.}
$$
= Solution
Using $A^3=I$, the matrix power reduces modulo three:
$$
\boxed{A^{3n+2}=A^2=\begin{pmatrix}0&0&1\\1&0&0\\0&1&0\end{pmatrix}.}
$$