25.  Which of the following statements are correct?

(A) If Q is orthogonal, then det(Q) = ±1. 

(B) Let A be a real n x n matrix. Then A is symmetric if and only if A is orthogonally equivalent to a real diagonal matrix.

(C) Let A ∈ be a matrix whose characteristic polynomial splits over . Then A is orthogonally equivalent to a real upper triangular matrix. 

(D) Let T be a self-adjoint (Hermitian) operator on a finite-dimensional inner product space V. Then every eigenvalue of T is positive.

(E) Let T be a self-adjoint (Hermitian) operator on a finite-dimensional inner product space V. Then every eigenvalue of T is negative.