Let T: Rn rightarrow Rm be a linear transformation. A right inverse for T is a linear transformation U Rm rightarrow Rn such that T(U(X)) = x for all x Rm. Show that T has a right inverse if and only if T is onto. A left inverse for T is a linear transformation U Rm rightarrow Rn such that U(T(x)) = x for all x Rn. Show that T has a left inverse if and only if T is one-to-one.