(a) If A = [-3, -2, -4; 2, 1, 2; 2, 1, 3], B = [1, 2, 0; -2, -1, -2; 0, -1, 1], then find AB and use it to solve the following system of equations: x…

If $\displaystyle \mathrm{A}=\left[\begin{array}{rrr}-3 & -2 & -4 \\ 2 & 1 & 2 \\ 2 & 1 & 3\end{array}\right], \mathrm{B}=\left[\begin{array}{rrr}1 & 2 & 0 \\ -2 & -1 & -2 \\ 0 & -1 & 1\end{array}\right]$, then find AB and use it to solve the following system of equations: \[\begin{aligned} & \mathrm{x}-2 \mathrm{y}=3 \\ & 2 \mathrm{x}-\mathrm{y}-\mathrm{z}=2 \\ & -2 \mathrm{y}+\mathrm{z}=3 \end{aligned} \]

If $\displaystyle f(\alpha)=\left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{array}\right]$, prove that $\displaystyle f(\alpha) \cdot f(-\beta)=f(\alpha-\beta)$