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.
- $$\left[ \begin{array} { c r } 12 & - 6 \\- 6 & 7\end{array} \right]$$

A)
$$P = \left[ \begin{array} { r r } 3 & 2 \\- 2 & 3\end{array} \right] , D = \left[ \begin{array} { r r } 16 & 0 \\0 & 3\end{array} \right]$$
B)
$$P = \left[ \begin{array} { r r } 3 / \sqrt { 13 } & - 2 / \sqrt { 13 } \\- 2 / \sqrt { 13 } & 3 / \sqrt { 13 }\end{array} \right] , D = \left[ \begin{array} { r r } 3 & 0 \\0 & 16\end{array} \right]$$
C)
$$P = \left[ \begin{array} { r r } 3 / \sqrt { 13 } & 2 / \sqrt { 13 } \\- 2 / \sqrt { 13 } & 3 / \sqrt { 13 }\end{array} \right] , D = \left[ \begin{array} { r r } 16 & 0 \\0 & 3\end{array} \right]$$
D)
$$P = \left[ \begin{array} { r r } 3 & - 2 \\- 2 & 3\end{array} \right] , D = \left[ \begin{array} { r r } 16 & 0 \\0 & 3\end{array} \right]$$