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 |
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
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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 |
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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 |
Option: B Explanation : Click on Discuss to view users comments. |
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 |
Option: B Explanation : Click on Discuss to view users comments. |
The inverse of - i in the multiplicative group, {1, - 1, i , - i} is
A. | 1 |
B. | -1 |
C. | i |
D. | -i |
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
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