The essential influence of the electron-hole (e-h) exchange Coulomb interaction on the properties of the two-dimensional magnetoexcitons was revealed. The main of them is the creation of two new symmetric and asymmetric superposition states formed by two bright magnetoexciton states with electron structure determined only by the direct Coulomb interaction and with the total angular momentum projections F=±1. The symmetric state due to the exchange e-h Coulomb interaction acquires a Dirac cone dispersion law in the range of small in-plane wave vectors with the group velocity proportional to the magnetic field strength B, with equal probabilities of the quantum transitions from the ground state of the crystal in both light circular polarizations but with maximum probability in the Faraday geometry of the light propagation and vanishing probability in the Voigt one. In difference on it, the asymmetric superposition state remains with the usual dispersion law inherited from the bare magnetoexciton states and has a dipole-active quantum transitions in both circular polarizations, indifferent on the direction of the light propagation. The both symmetric and asymmetric superposition states revealed the quantum interference effects in the case of the light with two linear polarizations, the vectors of which have different parities as regards the inversion of the light wave vector k→. The symmetric (asymmetric) state is allowed in the case of linear polarization vector with positive (negative) parity and is forbidden in the case of linear polarization vector with negative (positive) parity. The obtained optical results open the possibility to investigate the thermodynamic properties of the 2D Bose gas with Dirac cone dispersion law.