Let M be a given symmetric nxn real matrix. Let A be a linear operator on real antisymmetric n x n matrices given by AX = MXM

a) What is the largest possible number of complex eigenvalues that the operator A may have.

b) What is the largest possible number of eigenvalues of A that are not real?

Hint: use Frobenius inner product (M,K)=Tr(MK^{T})

Honestly, I don't know how to use the hint.

What is X? is it an arbitrary matrix? no special on it? Anyone explains me, please