Diagonalize the Matrix A, If Possible $$A = P D P^{ - 1}$$

Multiple Choice

Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that
$$A = P D P^{ - 1}$$
- $$A = \left[ \begin{array} { r r r } - 11 & 3 & - 9 \\0 & - 5 & 0 \\6 & - 3 & 4\end{array} \right]$$

A) $P = \left[ \begin{array} { r r r } 1 & 5 & - 1 \\ 5 & 3 & 0 \\ 1 & 3 & 1 \end{array} \right] , D = \left[ \begin{array} { r r r } - 5 & 1 & 0 \\ 0 & - 5 & 0 \\ 0 & 0 & - 2 \end{array} \right]$
B)
$$P = \left[ \begin{array} { r r r } 1 & 0 & - 1 \\5 & 3 & 0 \\1 & 1 & 1\end{array} \right] , D = \left[ \begin{array} { r r r } - 5 & 0 & 0 \\0 & - 5 & 0 \\0 & 0 & - 2\end{array} \right]$$
C)
$$\mathrm { P } = \left[ \begin{array} { r r r } 1 & 0 & - 1 \\0 & 3 & 0 \\1 & 1 & 1\end{array} \right] , \mathrm { D } = \left[ \begin{array} { r r r } - 5 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & - 2\end{array} \right]$$
D)
$$\mathrm { P } = \left[ \begin{array} { r r r } 1 & 0 & - 1 \\5 & 3 & 0 \\1 & 1 & 1\end{array} \right] , \mathrm { D } = \left[ \begin{array} { r r r } - 5 & 0 & - 2 \\0 & - 5 & 0 \\0 & - 5 & - 2\end{array} \right]$$