The sums vary from $0$ to $9$, thus there exist $10$ different values for the sum. Let us show that all $10$ values cannot be present simultaneously. Let us suppose that there is a row or a column with the sum $0$, thus all the cells of that row or column are zeroes. If it is a column, then the maximum value for the row is $8$. If it is a row, then in columns can be only values from $0$ to $4$. But then there can be $4$ more different values in rows. Together we have not more than $9$ different values. Example is shown on the picture (Fig. 20).