In a framework of a multi-phase transport model with both partonic and hadronic interactions, azimuthal correlations between trigger particles and associated scattering particles in Au + Au collisions at $sqrt{s_{NN}}$ = 200 GeV/$c$ have been studied by the mixing-event technique. The Mach-like structure has been observed in correlation function for central collisions. It is shown that the Mach-like structure is basically born in the partonic process and further developed in hadronic rescattering process. However, hadronic rescattering alone cannot reproduce the amplitude of Mach-like cone on away side, therefore partonic cascade process is necessary to describe the amplitude of Mach-like cone on away side in experiment. In addition, three-particle correlations have been investigated in central Au + Au collisions with the AMPT model, and the results support the conclusion that partonic cascade processes enhance the opening angle of Mach-like cone structures.