Commutative property

The commutative property is one of the three basic laws of regular algebras that greatly simplify equations and the derivation of their solutions. In essence, it assumes that one can commute, or interchange the positions of two variables $$x$$ and $$y$$ without changing the value of the result, (such as a product for multiplication, or a sum for addition), under an operation "$$*$$", that is: $$x * y = y * x .$$ Thus, commutativity can also be considered as a kind of symmetry caused by mirroring.

The associativity and distributivity laws are the other two simplifying properties of algebraic variables for operations such as multiplication and addition.