Is there an integer matrix with distinct entries and more than 2 rows with the property that every row sum is equal to every column product?
The matrix below has every row sum = 840 and every column product = 840, but it only has 2 rows. \begin{bmatrix}2&4&7&24&40&70&105&140&168&280\\420&210&120&35&21&12&8&6&5&3\end{bmatrix}