$3 \times 3$ 행렬 $A$ 가 $A \left (\begin{matrix*}[r] 1 \\ 1 \\ 1 \end{matrix*} \right) = \left (\begin{matrix*}[r] 2 \\ 2 \\ 2 \end{matrix*} \right), A \left (\begin{matrix*}[r] 2 \\ 0 \\ -1 \end{matrix*} \right) = \left (\begin{matrix*}[r] -2 \\ 0 \\ 1 \end{matrix*} \right)$ 을 만족할 때, $A ^ {4} \left (\begin{matrix*}[r] 1 \\ 5 \\ 7 \end{matrix*} \right)$ 의 값은?

• ①$\left (\begin{matrix*}[r] 76 \\ 80 \\ 82 \end{matrix*} \right)$
• ②$\left (\begin{matrix*}[r] 74 \\ 80 \\ 84 \end{matrix*} \right)$
• ③$\left (\begin{matrix*}[r] 75 \\ 81 \\ 83 \end{matrix*} \right)$
• ④$\left (\begin{matrix*}[r] 76 \\ 81 \\ 83 \end{matrix*} \right)$
• ⑤$\left (\begin{matrix*}[r] 75 \\ 79 \\ 83 \end{matrix*} \right)$