Question 92
In the cells of a square table the numbers $1$, $0$ or $-1$ are written in such a way that there is exactly one $1$ and exactly one $-1$ in every row and in every column. Is it always possible to obtain the opposite table by rearranging the rows and the columns of the initial table? (Two tables are called opposite if all the sums of the numbers in the corresponding cells equal $0$.)