10. Given

$A = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 2 & 1 \\ 0 & 0 & 3 \end{bmatrix} \text{ and } B = \begin{bmatrix} 2A & 2A \\ A & 3A \end{bmatrix},$

please find

a. (5 points) the eigenvalues of $A$,

b. (5 points) the corresponding eigenvectors of $A$, and

c. (5 points) the eigenvalues of $B$.