# Set Theory and Algebra MCQ - Algebra

1:

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

 A. multiplication is not a binary operation B. multiplication is not associative C. identity element does not exist D. zero has no inverse Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. zuhaib said: (3:10pm on Friday 24th February 2017) multiplication identity is '1' and additive edentity is '0'..thats right answer is '0' has no invers Kith said: (2:23pm on Wednesday 22nd March 2017) R-{0} is a group under multiplication Write your comments here:
2:

If (G, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ G, then G is a/an

 A. commutative semi group B. abelian group C. non-abelian group D. None of these Answer Report Discuss Option: B Explanation : For References Click Here Click on Discuss to view users comments. Write your comments here:
3:

image 113. If * is defined on R* as a * b = —ab/ 2,' then identity element in the group (R*., *) is

 A. 1 B. 2 C. 1/2 D. 1/3 Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
4:

If (G, .) is a group such that a2 = e,  ∀a ∈ G, then G is

 A. semi group B. abelian group C. non-abelian group D. none of these Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
5:

The inverse of - i in the multiplicative group, {1, - 1, i , - i} is

 A. 1 B. -1 C. i D. -i Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Amit kumar said: (5:57pm on Sunday 26th November 2017) As we know a.a^-1 =a^-1.a = e And 1 is the multiplicative identity element As (i ×-i )=1So i is the inverse element of i Write your comments here:

## Suggest an improvement

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