(a) If A = [1, 2, -2; -1, 3, 0; 0, -2, 1] and B^-1= [3, -1, 1; -15, 6, -5; 5, -2, 2], find ( AB )^-1.

$$\begin{aligned} & (\mathrm{a}) \mathrm{A}=\left[\begin{array}{rrr} 1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1 \end{array}\right], \mathrm{B}^{-1}=\left[\begin{array}{rrr} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{array}\right] \\ & (\mathrm{AB})^{-1}=\mathrm{B}^{-1} \mathrm{~A}^{-1} \\ & |\mathrm{~A}|=1(3)-2(-1)-2(2)=3+2-4=1 \neq 0 \end{aligned} $$ $$\therefore \mathrm{B}^{-1} \mathrm{~A}^{-1}=\left[\begin{array}{crr} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{array}\right]\left[\begin{array}{lll} 3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 2 & 5 \end{array}\right] $$