Commutative Law
Related Category: Mathematics
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.