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.