"Commutativity" is a property which an operation between two numbers (or other mathematical elements) may or may not have. The operation is commutative if it does not matter which element is named first.

For example, because addition is commutative, 5 + 7 has the same value as 7 + 5. Subtraction, on the other hand, is not commutative, and the difference 5 - 7 does not have the same value as 7 - 5.

Commutativity can be described more formally. If * stands for an operation and if A and B are elements from a given set, then * is commutative if, for all such elements A * B = B * A.

In ordinary arithmetic and algebra, the commutative operations are multiplication and addition. The non-commutative operations are subtraction, division, and exponentiation. For example, x + 3 is equal to 3 + x; xy is equal to yx; and (x + 7)(x - 2) is equal to (x - 2)(x + 7). On the other hand, 4 - 3x...