If (G, .) is a group, such that (ab)2 =a2b2 ∀ 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. |
Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an
| A. | subgroup |
| B. | finite abelian group |
| C. | infinite, non abelian group |
| D. | infinite, abelian |
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Option: C Explanation : Click on Discuss to view users comments. |
Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then
| A. | A is closed under * but < A, * > is not a semi group |
| B. | < A, * > is a semi group but not a monoid |
| C. | < A, * > is a monoid but not a group |
| D. | < A, * > is a group but not an abelian group |
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Option: D Explanation : Click on Discuss to view users comments. |
