Binary operation

This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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Definition

A binary operation on a set $X$ is a function $\ast :X\times X\to X$.

Examples

• Addition is a binary operation on the integers, rational numbers, real numbers and complex numbers.
• Matrix multiplication is a binary operation on the set of $n\times n$ matrices for any $n$.