Eigen vectors of $$\begin{bmatrix}1 & \cos \theta \\\cos \theta &1 \end{bmatrix}$$ are

A

$$\begin{bmatrix}a^{n} & 1 \\ 0 & a^{n} \end{bmatrix} $$

B

$$\begin{bmatrix}a^{n} &n \\ 0 & a^{n} \end{bmatrix} $$

C

$$\begin{bmatrix}a^{n} &n.a^{n-1} \\ 0 & a^{n} \end{bmatrix}$$

D

$$\begin{bmatrix}a^{n} &n.a^{n-1} \\ -n & a^{n} \end{bmatrix}$$