Consider the matrices -2 -1 1 4 1 A = B = 4 -2 4 -2 -2 4 -2 1 -1 (a) Verify that they are diagonalizable and that they commute. (b) Find the eigenvalues and eigenvectors of A and verify that its spectrum is nondegenerate. (c) Show that the eigenvectors of A are eigenvectors of B as well.
