  ## Encyclopedia > Commutative

Article Content

# Commutativity

Redirected from Commutative

In mathematics, especially abstract algebra, a binary operation * on a set S is commutative if, for all x and y in S, x * y = y * x.

The most commonly known examples of commutativity are addition and multiplication of natural numbers; for example:

• 4 + 5 = 5 + 4 (since both expressions evaluate to 9)
• 2 × 3 = 3 × 2 (since both expressions evaluate to 6)

Further examples of commutative binary operations include addition and multiplication of real and complex numbers, addition of vectors, and intersection and union of sets. Important non-commutative operations are the multiplication of matrices and the composition of functions.

An Abelian group is a group whose operation is commutative.

A ring is called commutative if its multiplication is commutative, since the addition is commutative in any ring.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia
 Search over one million articles, find something about almost anything!

Featured Article
 Lake Ronkonkoma, New York ... income for a household in the town is \$60,209, and the median income for a family is \$67,375. Males have a median income of \$50,715 versus \$34,301 for females. The per ...  