G Problem 1. (4 points) Suppose A is a matrix of size 5 by 5. Which of the following statements must be TRUE? (I) Eigenvalue of A can be zero, but eigenvector of A cannot be a zero vector. (II) If λ is an eigenvalue of A, then the nullity of A − λI must be at least one. (III) If det(A − λI) = −(λ − 5)2 (λ + 4)3 then λ = 5 is said to have algebraic multiplicity 2 and λ = −4 is said to have algebraic multiplicity 3. (A) I only (B) II only (C) III only (D) II and III only (E) I, II, and III