$2 \times 2$ 행렬 $A$ 가 $A \left (\begin{matrix*}[r] 1 \\ -1 \end{matrix*} \right) = \left (\begin{matrix*}[r] 2 \\ -2 \end{matrix*} \right), A \left (\begin{matrix*}[r] 1 \\ 1 \end{matrix*} \right) = \left (\begin{matrix*}[r] 3 \\ 3 \end{matrix*} \right)$ 을 만족할 때, $A ^ {17} \left (\begin{matrix*}[r] 11 \\ -5 \end{matrix*} \right) = \left (\begin{matrix*}[r] x \\ y \end{matrix*} \right)$ 라 놓으면 $x-y$ 의 값은?

• ①$2^ {19}$
• ②$2^ {21}$
• ③$3^ {19}$
• ④$3^ {21}$