A Commutative Operation is a function $f$ of two variables such that $f(a,b)=f(b,a).$

Operations are usually represented by writing a symbol between the two arguments. Examples include:

Subtraction and division are not commutative operations. They are "non-commutative."

A group in which the group operation is commutative is called an "Abelian Group."

AddingComplexNumbers DifferenceOfTwoSquares MatrixMultiplication MatrixTransformation Quaternion	(none)			(none)
↓	↓		↓	↓
Commutative			(none)
			↓
		⇌	You are here CommutativeOperation
			↓
			Function
↓	↓		↓	↓
(none)	(none)			CoDomainOfAFunction DomainOfAFunction ImageOfAFunction Polynomial RangeOfAFunction RealNumber

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Commutative Operation