Correct Option: C

Suppose the eigen value of matrix A is n
(= λ + i B_B) say.
and the eigen vector is n whereas the conjugate pair of eigen value and eigen vector is λ and n
So, An = λ n ...(1)
And An = λ n ...(2)
Taking transpose of equation
x^-TA^T = x^-Tλ ...(3)
⇒ x^-TA^T = x^-T⇒ x^-TAn = x^-T⇒ λ = λ
⇒ α + iβ = α - iβ
⇒ 2iβ = 0
⇒ β = 0
Hence eigen value of a symmetric matrix are real