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).
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The commutative property of addition and the commutative property of multiplication.
The commutative property of addition says that it does not matter in which order you add the numbers, you will get the same result. For example, 5 + 3 = 8 and 3 + 5 = 8.
The order in which the addends (in addition) or multiplicands (in multiplication) does not affect the answer. If symbolic form: a + b = b + a or a * b = b * a
The commutative property of multiplication says that the numbers in a problem can change, but the answer will stay the same.
The commutative property states that ab = ba.