The electromagnetic–acoustic field in a waveguide filled with a magnetoplasma (or in a stratified magnetoplasma), as well as the corresponding formally adjoint field, are decomposed into eigenmodes. The amplitudes of incoming and outgoing modes for both fields are related by scattering matrices. It is shown that the transposed scattering matrix of one field is the inverse scattering matrix of the other. The fictitious formally adjoint field is temporally mapped into a physical Lorentz-adjoint field, whose scattering matrix is shown to be the transpose of the scattering matrix of the original field.