Solutions to two problems of Dénes and Keedwell on row-complete latin squares

In a recent book, Dénes and Keedwell pose several questions concerning row-complete latin squares. Two of these questions are: (1) Is every row-complete latin square the Cayley table of a group? (2) Can every row-complete latin square be made column-complete by a suitable reordering of its rows? In the present paper, both questions are shown to have negative answers.