6. (20%) Let the matrix $\mathbf{A} = \begin{bmatrix} 3 & -1 & -2 \\ 2 & 0 & -2 \\ 2 & -1 & -1 \end{bmatrix}$. Answer the following questions:

(a) Find the eigenvalues and eigenvectors of the matrix \(\mathbf{A}\).