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The head-on collision between two magnetoacoustic solitons is investigated in a magnetized plasma containing inertial cold ions and warm electrons. A two-fluid magnetohydrodynamic (MHD) model is used to study the magnetoacoustic solitons interaction in plasmas. The magnetoacoustic wave dispersion effects appearing through electron inertial length (skin depth) are also included in the model. By using the extended Poincaré-Lighthill-Kuo (PLK) method, the Korteweg-de Vries (KdV) equations are derived for the low amplitude left and right moving magnetoacoustic solitons, their trajectories, and corresponding phase shifts after their elastic collisions are obtained analytically and examined numerically as well. It is found that only positive polarity (compressive) soliton structures of magnetoacoustic waves are formed. The profiles of head-on collision and the time evolution of two compressive interacting magnetoacoustic solitons are also presented for illustration. The effect of plasma beta, which depends on plasma density, electron temperature, and magnetic field intensity, on the phase shift of the interacting magnetoacoustic solitons is also examined.