The fact that antimatter and matter have the same mass is one of the basic principles of physics, and it has been confirmed by numerous experiments. One of the most famous experiments that confirmed this principle is the Millikan oil drop experiment, which was conducted by Robert Millikan in the early 20th century.
In the Millikan oil drop experiment, a small drop of oil is suspended in a vacuum chamber between two electrically charged plates. By carefully adjusting the voltage between the plates, Millikan was able to control the motion of the oil drop and measure its mass. He found that the mass of the oil drop was always the same, regardless of whether it was charged positively or negatively. This experiment demonstrated that the mass of an object is independent of its charge, and it provided strong evidence for the principle that antimatter and matter have the same mass.
Since the Millikan oil drop experiment, there have been many other experiments that have confirmed the principle that antimatter and matter have the same mass. These experiments have been conducted with a variety of different particles, including electrons, positrons, protons, and antiprotons. In all cases, the results have shown that antimatter and matter have the same mass.