I am trying to prove this problem:
Let M be the space of all 2 × 2 complex matrices, satisfying 〖(X)bar〗^t = -X (skew-hermitian).
Consider M as a vector space over R.
Define a bilinear form B on M by B(X,Y) = -tr(XY)
How should I show that B takes real values, is symmetric and positive definite?