In general, the rank of a product of matrices cannot exceed the rank of any factor in the product. Show that for two matrices A and B, rank AB cannot exceed the rank of A or the rank of B. a) Show that if B is n xp, then rank AB rank A. (Hint: Explain why every vector in the column space of AB is in the column space of A.) b) Show that if B is n xp, then rank AB rank B. (Hint: Use part a) and consider the rank of (AB)T.)