<P> In mathematics, a binary operation is commutative if changing the order of the operands does not change the result . It is a fundamental property of many binary operations, and many mathematical proofs depend on it . Most familiar as the name of the property that says "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings . The name is needed because there are operations, such as division and subtraction, that do not have it (for example, "3 − 5 ≠ 5 − 3"); such operations are not commutative, and so are referred to as noncommutative operations . The idea that simple operations such as the multiplication and addition of numbers are commutative, was for many years implicitly assumed . Thus, this property was not named until the 19th century, when mathematics started to become formalized . A corresponding property exists for binary relations; a binary relation is said to be symmetric if the relation applies regardless of the order of its operands; for example, equality is symmetric as two equal mathematical objects are equal regardless of their order . </P> <P> The commutative property (or commutative law) is a property generally associated with binary operations and functions . If the commutative property holds for a pair of elements under a certain binary operation then the two elements are said to commute under that operation . </P>

The commutative property only works under what two operations
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