In quantum mechanics, there is something called the Schrödinger equation. Quantum mechanics is really hard to ELI5, but the basic gist is that the equation is kinda like Newton’s Third Law – for every action there is an equal and opposite reaction – but applied to particles. For example, electrons are negatively charged, so there should exist an equivalent particle (the positron) which is positively charged. This logic is also extended to posit the existence of anti-protons and anti-neutrons.
Antimatter does exist, albeit in very tiny quantities and never for long. It is usually created through some kind of radioactive decay or particle accelerator. A rather common example is the potassium in a banana. About every 75 minutes a potassium atom decays, releasing a positron.
Should matter and antimatter ever interact, the result would be the conversion of matter into energy as they annihilate each other. If done with any meaningful mass, it would result in a very big boom.
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