8.9The commutator [X, Y] of two matrices is defined by the equation[X,Y] = XY - YX.Two anticommuting matrices A and B satisfyA² = 1,B² = 1,(a) Prove that C² = 1 and that [B, C] = 2iA.[A, B] = 2iC.

Given, The commutator X,Y of two matrices is defined by the equation X,Y = XY-YX. A2 = I, B2 = I,…

Answered: The commutator [X, Y] of two matrices…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.