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
$$A = P D P^{ - 1}$$
- $$A = \left[ \begin{array} { l l l } 2 & 0 & 0 \\1 & 2 & 0 \\0 & 0 & 2\end{array} \right]$$

A) $P = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 2 & 2 & 0 \\ 0 & 1 & 1 \end{array} \right] , D = \left[ \begin{array} { l l l } 2 & 1 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{array} \right]$
B)
$$P = \left[ \begin{array} { r r r } 1 & 0 & - 1 \\2 & 2 & 0 \\1 & 1 & 1\end{array} \right] , D = \left[ \begin{array} { l l l } 2 & 0 & 1 \\1 & 2 & 1 \\0 & 0 & 2\end{array} \right]$$
C) Not diagonalizable
D)
$$\mathrm { P } = \left[ \begin{array} { r r r } 1 & 2 & 1 \\0 & 2 & 1 \\- 1 & 0 & 1\end{array} \right] , \mathrm { D } = \left[ \begin{array} { l l l } 2 & 0 & 0 \\0 & 2 & 0 \\0 & 0 & 2\end{array} \right]$$