Please answer both questions for full rating

Question 2 (10 points). Let A = B = [138]. 1 U = (i) (2 points) Is B a left inverse of A? Justify your answer. (ii) (6 points) Find all left inverses of A, by letting L = a C be the left inverse. x y z You need to use elementary row operations, row echelon form, the reduced row echelon form. (iii) (1 points) Is Ar = u consistent? If yes, find the solution; if no, explain why. (iv) (1 points) Is Ax = v consistent? If yes, find the solution; if no, explain why. Question 3 (2 points). (True/False: if it is true, prove it; if it is false, give one counterexample). Let A be 2 x 3, and B be 3 x 2 matrices. If ABA = A, then BA =