A binary operation \(*\) is said to be commutative on a set if for any elements \(a\) and \(b\) in the set we have \(a*b=b*a\). In other words, the operation is commutative if the resulting value does not depend on the order of the operands. In arithmetic this is an important property of addition and multiplication of numbers.

Citation Info

  • [MLA] “commutative.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 3 Mar 2014. Web. 3 Mar 2014. <>
  • [APA] commutative (3 Mar 2014). Retrieved 3 Mar 2014 from the Platonic Realms Interactive Mathematics Encyclopedia:


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