Let A and B be two anticommuting matrices acting on a 2D vector space and satisfying the relation ² = ² = where I is the identity matrix.

a. Show that the eigenvalues of both matrices are 1.

b. Suppose are the normalized eigenvectors of the matrix A associated with the eigenvalues 1. i.e., | = |. If are the normalized eigenvectors of B associated with eigenvalues 1, then express as linear combinations of . Hint: Evaluating | may be helpful