Given A=(1234)A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}A=(1324), find the matrix XXX such that AX=(0110)AX = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}AX=(0110).
X=(12−0.51)X = \begin{pmatrix} 1 & 2 \\ -0.5 & 1 \end{pmatrix}X=(1−0.521)
X=(−1−20.51.5)X = \begin{pmatrix} -1 & -2 \\ 0.5 & 1.5 \end{pmatrix}X=(−10.5−21.5)
X=(0.5−1−0.250.5)X = \begin{pmatrix} 0.5 & -1 \\ -0.25 & 0.5 \end{pmatrix}X=(0.5−0.25−10.5)
X=(−110.50)X = \begin{pmatrix} -1 & 1 \\ 0.5 & 0 \end{pmatrix}X=(−10.510)