Binary Operation

Definition

A binary operation on a set $S$ means mapping the elements of $S\times S$ to $S$. In other words, it refers to a function $f$ : $S\times S\to S$. Given a binary operation $\ast$ : $S\times S\to S$, ${}_{(}a,b)$ is denoted as $a\ast b$.

Example

Let $Ma{t}_{2\times 2}(\mathbb{R})$ be the set of 2 × 2 real matrices. Then, the matrix multiplication $(A,B)\mapsto AB$ is a binary operation.