Linear Algebra

Which of the following statements are TRUE regarding the eigenvalues of real matrices?

Options:

• (A) A real symmetric matrix always has purely real eigenvalues
• (B) Eigenvectors corresponding to distinct eigenvalues of a real symmetric matrix are mutually orthogonal
• (C) A real skew-symmetric matrix has eigenvalues that are either zero or purely imaginary
• (D) If $\lambda$ is an eigenvalue of an invertible matrix $A$, then $1/\lambda$ is an eigenvalue of $A^{-1}$