What is the definition of the Commutative Property?

It means that in certain mathematical operations, you can turn around the order of the numbers without changing the result. Examples:

3 + 4 = 4 + 3 (addition of real numbers is commutative)

4 x 7 = 7 x 4 (multiplication of real numbers is commutative)

3 - 1 is not the same as 1 - 3 (subtraction is not commutative)

2 / 1 is not the same as 1 / 2 (division is not commutative)

For vectors, A x B = - B x A (not commutative; however, the vector cross product is anticommutative).

To help remember this property, think of the Word commuteor commuter (like when somebody moves from one place to another, like from home to work).