Let matrix $A=\left( \begin{matrix} {{{3}}} & {{{2}}} & {{{-2}}} \\ {{{-k}}} & {{{-1}}} & {{{k}}} \\ {{{4}}} & {{{2}}} & {{{-3}}} \\ \end{matrix} \right)$ exist, and let there be an invertible matrix $P$ such that $P^{-1}AP$ is a diagonal matrix. What then are $P$ and the corresponding diagonal matrix?

Options:
A. $$P=\left( \begin{matrix} {{{{}_{2}}}} & {{{{}_{1}}}} & {{{{}_{1}}}} \\ {{{{}_{2}}}} & {{{{}_{0}}}} & {{{{}_{0}}}} \\ {{{{}_{0}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ \end{matrix} \right) ,
P^{-1}AP = \left( \begin{matrix} {{-1}} & {{0}} & {{0}} \\ {{0}} & {{-1}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
B. $$P=\left( \begin{matrix} {{{{}_{1}}}} & {{{{}_{1}}}} & {{{{}_{1}}}} \\ {{{{}_{2}}}} & {{{{}_{0}}}} & {{{{}_{0}}}} \\ {{{{}_{0}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ \end{matrix} \right) ,
P^{-1}AP = \left( \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{0}} & {{-1}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
C. $$P=\left( \begin{matrix} {{{{}_{1}}}} & {{{{}_{1}}}} & {{{{}_{1}}}} \\ {{{{}_{2}}}} & {{{{}_{0}}}} & {{{{}_{0}}}} \\ {{{{}_{0}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ \end{matrix} \right) ,
P^{-1}AP = \left( \begin{matrix} {{-1}} & {{1}} & {{0}} \\ {{0}} & {{-1}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
D. $$P=\left( \begin{matrix} {{{{}_{1}}}} & {{{{}_{1}}}} & {{{{}_{-1}}}} \\ {{{{}_{2}}}} & {{{{}_{0}}}} & {{{{}_{0}}}} \\ {{{{}_{0}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ \end{matrix} \right) ,
P^{-1}AP = \left( \begin{matrix} {{-1}} & {{0}} & {{0}} \\ {{0}} & {{-1}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
E. $$P=\left( \begin{matrix} {{{{}_{1}}}} & {{{{}_{1}}}} & {{{{}_{1}}}} \\ {{{{}_{2}}}} & {{{{}_{0}}}} & {{{{}_{0}}}} \\ {{{{}_{0}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ \end{matrix} \right) ,
P^{-1}AP = \left( \begin{matrix} {{-1}} & {{0}} & {{0}} \\ {{0}} & {{1}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
F. $$P=\left( \begin{matrix} {{{{}_{1}}}} & {{{{}_{1}}}} & {{{{}_{1}}}} \\ {{{{}_{2}}}} & {{{{}_{0}}}} & {{{{}_{0}}}} \\ {{{{}_{0}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ \end{matrix} \right) ,
P^{-1}AP = \left( \begin{matrix} {{-1}} & {{0}} & {{0}} \\ {{0}} & {{-1}} & {{0}} \\ {{0}} & {{0}} & {{-1}} \\ \end{matrix} \right)
$$
G. $$P=\left( \begin{matrix} {{{{}_{-1}}}} & {{{{}_{1}}}} & {{{{}_{1}}}} \\ {{{{}_{2}}}} & {{{{}_{0}}}} & {{{{}_{0}}}} \\ {{{{}_{0}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ \end{matrix} \right) ,
P^{-1}AP = \left( \begin{matrix} {{-1}} & {{0}} & {{0}} \\ {{0}} & {{-1}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
H. $$P=\left( \begin{matrix} {{{{}_{1}}}} & {{{{}_{-1}}}} & {{{{}_{1}}}} \\ {{{{}_{2}}}} & {{{{}_{0}}}} & {{{{}_{0}}}} \\ {{{{}_{0}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ \end{matrix} \right) ,
P^{-1}AP = \left( \begin{matrix} {{-1}} & {{0}} & {{0}} \\ {{0}} & {{-1}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
I. $$P=\left( \begin{matrix} {{{{}_{1}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ {{{{}_{2}}}} & {{{{}_{0}}}} & {{{{}_{0}}}} \\ {{{{}_{0}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ \end{matrix} \right) ,
P^{-1}AP = \left( \begin{matrix} {{-1}} & {{0}} & {{0}} \\ {{0}} & {{-1}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
J. $$P=\left( \begin{matrix} {{{{}_{1}}}} & {{{{}_{1}}}} & {{{{}_{1}}}} \\ {{{{}_{2}}}} & {{{{}_{0}}}} & {{{{}_{0}}}} \\ {{{{}_{0}}}} & {{{{}_{2}}}} & {{{{}_{1}}}} \\ \end{matrix} \right) ,
P^{-1}AP = \left( \begin{matrix} {{-1}} & {{0}} & {{0}} \\ {{0}} & {{-1}} & {{0}} \\ {{0}} & {{0}} & {{1}} \\ \end{matrix} \right)
$$
Answer: J