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. | ininite, 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 = a where ab = a (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. |
