In arithmetic, operations are interchangeable if they are commutative

Yes it is : a + b = b + a for all integers a and b. In fact , if an operation is called addition you can bet that it is commutative. It would be perverse to call an non-commutative operation addition.

division and subtraction

Addition and Multiplication

Subtraction and division.

Division and subtraction cannot be used with the commutative property.

Yes. The commutative property of addition (as well as the commutative property of multiplication) applies to all real numbers, and even to complex numbers. As an example (for integers): 5 + (-3) = (-3) + 5

Addition & multiplication

Yes. The additive identity is always commutative - even in sets with binary operations that are not otherwise commutative.

addition and multiplication

That's commutative ... 3x2 = 2x3.

Because 9 - 7 does not equal 7 - 9.

No. It is not a group.

Addition and multiplication

It works for some operations, for others it doesn't. Specifically, both addition and multiplication of real numbers are commutative.

In math, the Commutative Property refers to operations in which the order of the numbers being operated on does not matter. Multiplication and addition are commutative operations, which may be demonstrated by the algebraic equations "ab = ba" and "a + b = b + a", respectively.

The multiplication most people are familiar with which you probably learned in school, IS commutative - that's the multiplication of integers, as well as real numbers in general.There are some other operations which mathematicians call "multiplication" which are NOT communitative; for example, the multiplication of matrices, or the cross-product of vectors.

The question cannot be answered because there is no justification for assuming that the operations are multiplication and also that the operations are commutative.

fundamental operation is a ?

Commutativity is a property of binary operations. A fact is not a binary operator.

Try it out. 3 + 9 = 9 + 3 That works. 3 x 9 = 9 x 3 That works. 3 - 9 = 9 - 3 That doesn't work. 3/9 = 9/3 That doesn't work. The numbers came first. The commutative law was only devised because of the relationship of the numbers. It isn't that the commutative property doesn't work for other operations, it's that the other operations aren't commutative.

They are not the same!The set of integers is closed under multiplication but not under division.Multiplication is commutative, division is not.Multiplication is associative, division is not.

Numbers, by themselves are neither commutative nor are they non-commutative. Commutativity is a property that belongs to a mathematical operation on a set of numbers. However, since the question does not specify what operation you have in mind, it is not possible to give a more helpful answer. The basic operations of arithmetic are addition, subtraction, multiplication and division, but there are many more mathematical operations.

The property that multiplication of integers is commutative.

No because the commutative property only works for addition and multiplication

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