Question

: Linear Algebra: Let A be an nxn matrix and let B = I - 2A + A^2. Let x be an eigenvector of A corresponding to an eigenvalue L, and that same x also be an eigenvector of B corresponding to an eigenvalue U, i.e. Ax = Lx and Bx = Ux. Show that if L = 1 is an eigenvector of A, then the matrix B will be singular.