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.
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.
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