Definition

Multiplication is a fast way to add equal groups: instead of adding the same number over and over, you multiply to get the answer quickly, and the result is called the product. As a binary operation on numbers, for positive integers $a \times b$ is the sum of $b$ copies of $a$, with key properties commutative ($a \times b = b \times a$), associative ($(a \times b) \times c = a \times (b \times c)$), distributive over addition ($a \times (b + c) = a \times b + a \times c$), and identity element $1$. Multiplication is one of the two operations defining a ring $(R, +, *)$, requiring that $*$ is associative, distributes over $+$, and has an identity; commutativity is an additional property that $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$, and $\mathbb{C}$ all satisfy, while matrix multiplication does not.