## MCQs of Group Theory

**1. This is an abelian group { – 3 n : n ε Z } under?**

A. division

B. subtraction

C. addition

D. multiplication

**2. What is the inverse of – ι If G = { 1, -1, ι, – ι } is group under multiplication?**

A. −1

B. ι

C. 1

D. None of Above

**3. The monoid is a?**

A. a non-abelian group

B. groupoid

C. A group

D. a commutative group

**4. (**ba**)-1 =_____ If a, b are elements of a group G?**

A. b-1 a

B. a-1 b

C. b-1 a-1

D. a-1 b-1

**5. What is an inverse of – **i** in the multiplicative group if {1, – 1, **i ,** – i} is?**

A. -1

B. 1

C. i

D. None of these

**6. What is the value of (a- 1 b)- 1 is in the group (G, .)?**

A. b- 1a

B. ab-1

C. ba-1

D. a-1b

**7. What is the inverse of an if (Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z? **

A. -2

B. 0

C. -a-2

D. a-2

**8. Which sentence is true? **

A. Set of all matrices forms a group under multiplication

B. Set of all rational negative numbers forms a group under multiplication

C. Set of all non-singular matrices forms a group under multiplication

D. Both (b) and (c)

**9. Which statement is false?**

A. The set of rational integers is an abelian group under addition

B. The set of rational numbers form an abelian group under multiplication

C. The set of rational numbers is an abelian group under addition

D. None of these

**10. What is the identity element In the group G = {2, 4, 6, 8) under multiplication modulo 10? **

A. 5

B. 9

C. 6

D. 12