행렬 $A$ 가 $A \begin{bmatrix*}[r] 1 \\ 0 \\ 0 \end{bmatrix*} = \begin{bmatrix*}[r] 1 \\ 1 \\ 1 \end{bmatrix*}$, $A \begin{bmatrix*}[r] 0 \\ 2 \\ 0 \end{bmatrix*} = \begin{bmatrix*}[r] 1 \\ 2 \\ 3 \end{bmatrix*}$, $A \begin{bmatrix*}[r] 0 \\ 0 \\ 3 \end{bmatrix*} = \begin{bmatrix*}[r] 1 \\ -1 \\ 1 \end{bmatrix*}$ 을 만족할 때, $A ^ {-1}$ 의 $\left (2, 3 \right)$ 성분은?

• ①$-1$
• ②$\displaystyle \frac{4} {9}$
• ③$\displaystyle \frac{2} {3}$
• ④$1$
• ⑤$\displaystyle \frac{4} {3}$