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Welcome to the Group Theory MCQs Page

Dive deep into the fascinating world of Group Theory with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Group Theory, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Group Theory, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

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Check out the MCQs below to embark on an enriching journey through Group Theory. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Group Theory. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Group Theory MCQs | Page 4 of 9

Explore more Topics under Discrete Mathematics

Q31.
In a group there must be only __________ element.

a.

1

b.

2

c.

3

d.

5

Discuss
Answer: (a).1
Q32.
_____ is the multiplicative identity of natural numbers.

a.

0

b.

-1

c.

1

d.

2

Discuss
Answer: (c).1
Q33.
An identity element of a group has ______ element.

a.

associative

b.

commutative

c.

inverse

d.

homomorphic

Discuss
Answer: (c).inverse
Q34.
__________ matrices do not have multiplicative inverses.

a.

non-singular

b.

singular

c.

triangular

d.

inverse

Discuss
Answer: (b).singular
Q35.
If X is an idempotent nonsingular matrix, then X must be ___________

a.

singular matrix

b.

identity matrix

c.

idempotent matrix

d.

nonsingular matrix

Discuss
Answer: (b).identity matrix
Q36.
If A, B, and C are invertible matrices, the expression (AB⁻¹)⁻¹(CA⁻¹)⁻¹C2 evaluates to ____________

a.

BC

b.

C⁻¹BC

c.

AB⁻¹

d.

C⁻¹B

Discuss
Answer: (a).BC
Q37.
If the sum of elements in each row of an n×n matrix Z is zero, then the matrix is ______________

a.

inverse

b.

non-singular

c.

additive inverse

d.

singular

Discuss
Answer: (d).singular
Q38.
___________ are the symmetry groups used in the Standard model.

a.

lie groups

b.

subgroups

c.

cyclic groups

d.

poincare groups

Discuss
Answer: (a).lie groups
Q39.
A semigroup S under binary operation * that has an identity is called __________

a.

multiplicative identity

b.

monoid

c.

subgroup

d.

homomorphism

Discuss
Answer: (b).monoid
Q40.
An element a in a monoid is called an idempotent if ______________

a.

a⁻¹=a*a⁻¹

b.

a*a²=a

c.

a²=a*a=a

d.

a³=a*a

Discuss
Answer: (c).a²=a*a=a
Page 4 of 9

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