Linear preservers of matrices of rank-2

Let T be a linear operator on the space of all m x n matrices over any fiel d. We prove that if T maps rank-2 matrices to rank-2 matrices then there ex ist nonsingular matrices U and V such that either T(X) = UX V for all matri ces X, or m = n and T(X) = (UXV)-V-t for all matrices X where X-t denotes t he transpose of X.