5. Given the following matrix.
$A = \begin{bmatrix} 0 & 4 & -2 \\ -3 & 5 & 0 \\ -3 & 1 & 4 \end{bmatrix}$.
1) Find all the Eigenvalues.
2) Diagonalize matrix $A$.
6. Show that if $A$ is both diagonalizable and invertible, then so is $A^{-1}$. (Provide your reasoning.)
7. Find a unit vector in the direction of $\begin{bmatrix} 4 \\ -12 \\ -4 \end{bmatrix}$.