An n x n complex matrix A is called skew-hermitian if and only if: A = -A. A real, skew-hermitian matrix is called anti-symmetric or skew-symmetric. a) Let A be a skew-hermitian matrix and suppose A E C is an eigen- value of A. Prove that = ib, with b E R. (Hint: Mimic the proof done in class to show that the eigenvalues of a Hermitian matrix are all real.) b) Let A be a real, skew-symmetric matrix, prove that if X ER is an eigenvalue, then = 0. c) Prove that if n is odd, then 0 is always an eigenvalue of A. d) Find all eigenvalues and eigenvectors for the skew-symmetric matrices: = (-28) A = = A 42 = ( 3 0 -3 0-4 4 0