(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 |
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 |
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 |
Option: D Explanation : Click on Discuss to view users comments. |
If a, b are positive integers, define a * b = α where ab = α (modulo 7), with this * operation, then inverse of 3 in group G (1, 2, 3, 4, 5, 6) is
A. | 3 |
B. | 1 |
C. | 5 |
D. | 4 |
Option: C Explanation : Click on Discuss to view users comments. |
Which of the following is TRUE ?
A. | Set of all rational negative numbers forms a group under multiplication |
B. | Set of all non-singular matrices forms a group under multiplication |
C. | Set of all matrices forms a group under multipication |
D. | Both (b) and (c) |
Option: B Explanation : Click on Discuss to view users comments. |