Given matrices $\underline{A}$, and $\underline{B}$ find the following:
$\underline{A} = \begin{pmatrix} 3 & 5 & -4 \\ -3 & -2 & 4 \\ 6 & 1 & -8 \end{pmatrix}$, $\underline{B} = \begin{pmatrix} 1 & 1 & -1 \\ -1 & -2 & 4 \\ 6 & 1 & -0 \end{pmatrix}$, $\underline{b} = \begin{pmatrix} 7 \\ -1 \\ -4 \end{pmatrix}$
1. $\underline{A} \cdot \underline{B}$
2. Find $\underline{B}^{-1}$ using row-reduction.
3. $\underline{A} - 2\underline{B}$
4. $det(\underline{A} + \underline{B})$
5. $det(\underline{A}^4)$
6. Verify that $det(\underline{A} \cdot \underline{B}) = det(\underline{B} \cdot \underline{A})$
7. Is $\underline{B}$ a symmetric matrix? If not, symmetrize it.
8. Solve the equation $\underline{B} \cdot \underline{x} = \underline{b}$ using any method.
