RU-ALLRUSSIAN 1982 Problem 19

An $\mathrm{n} \times \mathrm{n}$ array has a cross in $\mathrm{n} - 1$ cells. A move consists of moving a row to a new position or moving a column to a new position. For example, one might move row 2 to row 5, so that row 1 remained in the same position, row 3 became row 2, row 4 became row 3, row 5 became row 4, row 2 became row 5 and the remaining rows remained in the same position. Show that by a series of moves one can end up with all the crosses below the main diagonal.