Orthogonally Diagonalize the Matrix, Giving an Orthogonal Matrix P and a Diagonal

Multiple Choice

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D.
- $$\left[ \begin{array} { r r r } 11 & 7 & 7 \\7 & 11 & 7 \\7 & 7 & 11\end{array} \right]$$

A)
$$P = \left[ \begin{array} { c c c } 1 / \sqrt { 3 } & - 1 / \sqrt { 2 } & - 1 / \sqrt { 6 } \\1 / \sqrt { 3 } & 1 / \sqrt { 2 } & - 1 / \sqrt { 6 } \\1 / \sqrt { 3 } & 0 & 2 / \sqrt { 6 }\end{array} \right] , D = \left[ \begin{array} { r r r } 4 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 25\end{array} \right]$$
B)
$$P = \left[ \begin{array} { r r r } 1 & - 1 & - 1 \\1 & 1 & - 1 \\1 & 0 & 2\end{array} \right] , D = \left[ \begin{array} { r r r } 25 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 4\end{array} \right]$$
C)
$$P = \left[ \begin{array} { r c c } 1 / \sqrt { 3 } & 1 / \sqrt { 2 } & 1 / \sqrt { 6 } \\1 / \sqrt { 3 } & - 1 / \sqrt { 2 } & 1 / \sqrt { 6 } \\- 1 / \sqrt { 3 } & 0 & 2 / \sqrt { 6 }\end{array} \right] , D = \left[ \begin{array} { r r r } 25 & 0 & 0 \\0 & 25 & 0 \\0 & 0 & 4\end{array} \right]$$
D)
$$P = \left[ \begin{array} { c c c } 1 / \sqrt { 3 } & - 1 / \sqrt { 2 } & - 1 / \sqrt { 6 } \\1 / \sqrt { 3 } & 1 / \sqrt { 2 } & - 1 / \sqrt { 6 } \\1 / \sqrt { 3 } & 0 & 2 / \sqrt { 6 }\end{array} \right] , D = \left[ \begin{array} { r r r } 25 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 4\end{array} \right]$$