For a strictly complex matrix $A$,
1) Can we comment on determinant of $A^{*}$ (conjugate of entries of $A$) , $A^{T}$ (transpose of A) and $A^{H}$ (hermitian of $A$). I know that for real matrices, $\det(A)=\det(A^{T})$. Does it carry over to complex matrices, i.e. does $\det(A)=\det(A^{T})$ in general? I understand $\det(A)=\det(A^{H})$ (from Schur triangularization).
2) The same question as first, now about eigenvalues of $A$. I would like to know about special cases, for instance what if $A$ is hermitian or positive definite and so on.