Let A be an m x n matrix, show that the following are equivalent:
(a) A has a right inverse, that is, there exists an n x m matrix C such that AC=I.
(b) The system Ax=b has at least one solution x for each b in Rm.
(c) The columns of A span Rm.
Show that any one of (a),(b) or (c) implies that m<=n.
Thanks very much.