다음 중 모든 열벡터 $x, y \in ℝ^2$ 에 대하여 $\left \| Ax-Ay \right \| = \left \| x-y \right \|$ 인 행렬 $A$ 는? (단, $\left \| \left (\begin{matrix*}[r] a \\ b \end{matrix*} \right) \right \| = \sqrt {a^2 +b^2}$)

• ①$\displaystyle \frac{1} {\sqrt {2}} \begin{pmatrix*}[r] 1 & 1 \\ 1 & 1 \end{pmatrix*}$
• ②$\displaystyle \frac{1} {\sqrt {2}} \begin{pmatrix*}[r] 1 & 1 \\ 1 & -1 \end{pmatrix*}$
• ③$\displaystyle \frac{1} {\sqrt {2}} \begin{pmatrix*}[r] 1 & 0 \\ 1 & 2 \end{pmatrix*}$
• ④$\displaystyle \frac{1} {\sqrt {2}} \begin{pmatrix*}[r] 1 & 0 \\ 1 & -2 \end{pmatrix*}$