Let AAA be a 2×22 \times 22×2 matrix such that A(11)=(22)A \begin{pmatrix} 1 \\ 1 \end{pmatrix} = \begin{pmatrix} 2 \\ 2 \end{pmatrix}A(11)=(22) and A(1−1)=(−33)A \begin{pmatrix} 1 \\ -1 \end{pmatrix} = \begin{pmatrix} -3 \\ 3 \end{pmatrix}A(1−1)=(−33). What is the matrix AAA?
(−0.52.52.5−0.5)\begin{pmatrix} -0.5 & 2.5 \\ 2.5 & -0.5 \end{pmatrix}(−0.52.52.5−0.5)
(0.51.51.50.5)\begin{pmatrix} 0.5 & 1.5 \\ 1.5 & 0.5 \end{pmatrix}(0.51.51.50.5)
(2−3−32)\begin{pmatrix} 2 & -3 \\ -3 & 2 \end{pmatrix}(2−3−32)
(−133−1)\begin{pmatrix} -1 & 3 \\ 3 & -1 \end{pmatrix}(−133−1)