The set of all real numbers under the usual multiplication operation is not a group since

multiplication is not a binary operation

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multiplication is not associative

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identity element does not exist

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zero has no inverse

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Solution

The correct option is D zero has no inverse
Set of real number i.e. $(- \infty, 0) \cup (0, \infty)$ is under usual multiplication operation because $0 \in R$ and zero do not have an inverse i.e. it can not give ordered airs to be included in a group.

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Similar questions

Which of the following is not a binary operation defined on the set of positive real numbers?

Which of the following binary operations defined on the set of real numbers is not associative?

a * b = \frac{a + b}{2}

*

a * b = 2^{a b}

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