Let GL(2, 11) be the group of all invertible 2 x 2 matrices with entries in Z₁1, with group operation given my matrix multiplication. Consider the following two matrices in this group (where an entry listed as k is shorthand for [k]11): 3 10 A = (₁ 10), B = (3 ¹18). 1 8 (i) Show that A has order 5, B has order 2, and that BAB-¹ = A−¹.
Let GL(2, 11) be the group of all invertible 2 x 2 matrices with entries in Z₁1, with group operation given my matrix multiplication. Consider the following two matrices in this group (where an entry listed as k is shorthand for [k]11): 3 10 A = (₁ 10), B = (3 ¹18). 1 8 (i) Show that A has order 5, B has order 2, and that BAB-¹ = A−¹.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 15E: 15. Repeat Exercise with, the multiplicative group of matrices in Exercise of Section.
14. Let be...
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 39 images
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning