24. Let i (i = 1, 2, ..., r) be the nonzero characteristic roots of an...

24. Let λ_i (i = 1, 2, ..., r) be the nonzero characteristic roots of an m x m symmetric matrix A. Show that λ_i^-1 (i = 1, 2, ..., r) are the nonzero characteristic roots of A^-1.