Time complexity of optimal algorithm for solving this problem
$O(n^2 log n)$ is easy: Create a sorted array of the items in the first row. Lookup the items in the second row in this array using binary search, and remove items that were not present. Same with the third row etc. The last remaining item is the largest one present in evert row. The main effort is $n^2$ lookups in an array of size n.

Using a hash table probably makes it $O (n^2)$.