Questions
21
(Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z. The inverse of a is
Answer: -a-2
22
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
Answer: infinite, non abelian group
23
Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then
Answer: < A, * > is a group but not an abelian group
25
If G = { 1, -1, ι, - ι } is group under multiplication, then inverse of - ι is
Answer: ι
30
What is the inverse of – ι If G = { 1, -1, ι, – ι } is group under multiplication?
Answer: ι
32
What is an inverse of – i in the multiplicative group if {1, – 1, i , – i} is?
Answer: i
34
What is the inverse of an if (Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z?
Answer: -a-2
35
Which sentence is true?
Answer: Set of all non-singular matrices forms a group under multiplication
36
Which statement is false?
Answer: The set of rational numbers form an abelian group under multiplication
37
What is the identity element In the group G = {2, 4, 6, 8) under multiplication modulo 10?
Answer: 6
38
Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?
Answer: None of these
39
Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?
Answer: (g o h) 2 = g2o h2 for every g,h ∈ G
