Matrix MOC based on modular ray tracing consuming less memory for geometrical information was studied. Method making use of the symmetry of problems based on modular ray tracing was proposed which reduces memory demands and improves efficiency furthermore. The numeric properties of the coefficient matrix were dug out by analysis of the construction process, due to which constructing computation and memory demand can be reduced significantly. In case of upscatter, multi-group GMRES based on Matrix MOC and its numeric properties was studied for accelerating the multi-group iterations.