a.) Prove that if A 0 and B 0, then AB 0, assuming that the product AB is defined. b.) (5 points) Prove that if A 0 and B 0, then AB 0, assuming that the product AB is defined. c.) (5 points) Prove that if A 0 and B 0, then AB 0, assuming that the product AB is defined. d.) (5 points) Prove that if A 0 and B C, then AB AC, assuming that all the products are defined. e.) (5 points) Prove that if A 0 and B C, then AB AC, assuming that all the products are defined. f.) (3 points) Prove or disprove that A 0 for all square matrices A. g.) (3 points) Prove or disprove that ATA 0 for all square matrices A. h.) (3 points) Prove or disprove that for all invertible square matrices A for which A 0, then A 0. 1