Question

A = \begin{bmatrix} 2 & -2 \\ -2 & 3 \end{bmatrix} and B = \begin{bmatrix} 5 & -3 \\ 2 & -1 \end{bmatrix}. \\ (a) Find AB, A^{-1}, and B^{-1}. \\ AB = \begin{bmatrix} 6 & -4 \\ -4 & 3 \end{bmatrix} \\ A^{-1} = \begin{bmatrix} 3/2 & 1 \\ 1 & 1 \end{bmatrix} \\ B^{-1} = \begin{bmatrix} -1 & 3 \\ -2 & 5 \end{bmatrix} \\ (b) Show that (AB)^{-1} = B^{-1}A^{-1}. \\ (AB)^{-1} = \\ B^{-1}A^{-1} =

          A = \begin{bmatrix} 2 & -2 \\ -2 & 3 \end{bmatrix} and B = \begin{bmatrix} 5 & -3 \\ 2 & -1 \end{bmatrix}. \\
(a) Find AB, A^{-1}, and B^{-1}. \\
AB = \begin{bmatrix} 6 & -4 \\ -4 & 3 \end{bmatrix} \\
A^{-1} = \begin{bmatrix} 3/2 & 1 \\ 1 & 1 \end{bmatrix} \\
B^{-1} = \begin{bmatrix} -1 & 3 \\ -2 & 5 \end{bmatrix} \\
(b) Show that (AB)^{-1} = B^{-1}A^{-1}. \\
(AB)^{-1} = \\
B^{-1}A^{-1} =