In this paper we studied the Maxwell's equations in imhomogeneous and anisotropic media as an operator. It is defined in a bounded region, which can be comprehended as a resonant cavity in micro-wave technique. But these cavities are filled with ferrite, plasma or other gyrotropic medium, all these new media become more and more important in practice. We proved that under some concrete conditions imposed on μ, ε and restrictions on the boundary value, the operator of Maxwell's equations becomes a symmetric one. The symmetry and self-adjoint property give much convenience in eigenfunction expansion problems. Besides, we derived the orthogonality of characteristic oscillation and reciprocity theorem in general.If it does not satisfy the conditions of symmetry, we introduced the concept of adjoint-cavity. The so-called adjoint cavity coincides with the primary cavity in geometrical shape, but both μ, ε and boundry conditions do not coincide. It has some properties similiar with self-adjoint cavity in orthogonality and reciprocity theorem.