# commutative law

Also found in: Dictionary.

## commutative law,

in mathematics, law holding that for a given binary operation (combining two quantities) the order of the quantities is arbitrary; e.g., in addition, the numbers 2 and 5 can be combined as 2+5=7 or as 5+2=7. More generally, in addition, for any two numbers*a*and

*b*the commutative law is expressed as

*a*+

*b*=

*b*+

*a.*Multiplication of numbers is also commutative, i.e.,

*a*×

*b*=

*b*×

*a.*In general, any binary operation, symbolized by +, joining mathematical entities

*A*and

*B*obeys the commutative law if

*A*+

*B*=

*B*+

*A*for all possible choices of

*A*and

*B.*Not all operations are commutative; e.g., subtraction is not since 2−5≠5−2, and division is not since 2-5≠ 5-2.

The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/

## commutative law

[¦käm·yə‚tād·iv ‚lȯ] (mathematics)

A rule which requires that the result of a binary operation be independent of order; that is,

*ab*=*ba*.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

Want to thank TFD for its existence? Tell a friend about us, add a link to this page, or visit the webmaster's page for free fun content.

Link to this page: