The set of integers Z with the binary operation "*" defined as a*b =a +b+ 1 for a, b ∈ Z, is a group. The identity element of this group is
| A. | 0 |
| B. | 1 |
| C. | -1 |
| D. | 12 |
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Option: C Explanation : Click on Discuss to view users comments. |
In the group (G, .), the value of (a- 1 b)- 1 is
| A. | ab-1 |
| B. | b- 1a |
| C. | a-1b |
| D. | ba-1 |
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Option: B Explanation : Click on Discuss to view users comments. |
114. The identity element in the group
G={[x x]}:x €R,x#0} with respect to matrix
{[x x]}
multiplication is
| A. | (1/0 0/1) |
| B. | (-1/0 0/-1) |
| C. | ((1/2)/(1/2) (1/2)/(1/2)) |
| D. | (1/1 1/1) |
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Option: C Explanation : Click on Discuss to view users comments. |
If (G, .) is a group, such that (ab)2 = a2 b2 ∀ 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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Option: B Explanation : Click on Discuss to view users comments. |
(Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z. The inverse of a is
| A. | 0 |
| B. | -2 |
| C. | a-2 |
| D. | -a-2 |
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Option: D Explanation : Click on Discuss to view users comments. sachin kushare said: (4:15pm on Monday 25th February 2013)
we have a*e=a....(Identity property)so, a e 1=aso, e=-1we have a*b=-1....(Inverse property)so, a b 1=-1 b=-2-aso correct option (D)
Simran said: (1:49pm on Tuesday 27th June 2017)
Inverse : let a.(-a-2) = a (-a-2) 1= -1 = etherefore a inverse = -a-2 for all a belongs to Z
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