The commutator [X, Y] of two matrices is defined by the equation [X, Y] = XY - YX. Two anticommuting matrices A and B satisfy A² = 1₂ B² = 1, (a) Prove that C² = 1 and that [B, C] = 2iA. [A, B] = 2iC.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 72E: Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.
icon
Related questions
Question
100%
8.9
The commutator [X, Y] of two matrices is defined by the equation
[X,Y] = XY - YX.
Two anticommuting matrices A and B satisfy
A² = 1,
B² = 1,
(a) Prove that C² = 1 and that [B, C] = 2iA.
[A, B] = 2iC.
Transcribed Image Text:8.9 The commutator [X, Y] of two matrices is defined by the equation [X,Y] = XY - YX. Two anticommuting matrices A and B satisfy A² = 1, B² = 1, (a) Prove that C² = 1 and that [B, C] = 2iA. [A, B] = 2iC.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax