Interesting Intersection

An $m \times n$ array $A$ of real numbers is an Intersecting array if for all $i$, $j$, $k$ and $l$ such that $0 \leq i \lt k \lt m$ and $0 \leq j \lt l \lt n$, we have $A[i, j] + A[k, l] \leq A[i, l] + A[k, j]$ In other words, whenever we pick two rows and two columns of an Intersecting array and consider the four elements at the intersections of the rows and columns, the sum of the upper-left