Predicted by the Dirac equation.
Can be easily seen from the solution of Equation "Expanded Dirac equation in Planck units" when the particle is at rest as shown at Video "Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)".
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Antimatter consists of antiparticles, whose rest masses and spins match those of the corresponding particles while additive internal conserved charges are reversed. A Positron, for example, has the electron's rest mass and opposite electric charge. Both have positive physical energy.
When a particle meets its antiparticle, annihilation can convert the pair into other particles while preserving total energy, momentum and applicable conserved charges. Electron-positron annihilation into two photons is a simple example. Producing a few antiparticles in energetic collisions does not establish a large cosmological antimatter population: the production process and the subsequent abundance are separate questions. The antiparticle description is built into relativistic quantum field theory, rather than requiring negative measured mass or energy.
Antimatter is a type of matter composed of antiparticles, which have the same mass as particles of ordinary matter but opposite electric charge and other quantum properties. For example, the antiparticle of the electron is the positron, which carries a positive charge instead of a negative one. Similarly, the antiproton is the antiparticle of the proton and has a negative charge.