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The associative and commutative are properties of operations defined on mathematical structures.

Both properties are concerned with the order - of operators or operands.

According to the ASSOCIATIVE property, the order in which the operation is carried out does not matter. Symbolically, (a + b) + c = a + (b + c) and so, without ambiguity, either can be written as a + b + c.

According to the COMMUTATIVE property the order in which the addition is carried out does not matter. In symbolic terms, a + b = b + a

For real numbers, both addition and multiplication are associative and commutative while subtraction and division are not. There are many mathematical structures in which a binary operation is not commutative - for example matrix multiplication.

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Q: How are the associative and commutative properties alike and different?
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