3. Given the following matrix $A$
$
A=\left[\begin{array}{lll}
2 & 1 & 0 \\
0 & 2 & 0 \\
0 & 0 & 2
\end{array}\right]
$
(a) How many distinct eigenvalues does $A$ have?
(b) Find all the eigenvalues and eigenvectors of $A$. Name the free variables as $t_1$, $t_2$, so on so forth.
(c) Find $A^{-1}$. If $A$ is singular, specify the reason.
Hint: $\left[\begin{array}{ll}A & \mathbf{I}_{3 \times 3}\end{array}\right] \sim\left[\begin{array}{ll}\mathbf{I}_{3 \times 3} & A^{-1}\end{array}\right]$