Every pair of congruent cells is either equivalent or differs in value by n2. All cell pairs congruent to a row's seed column's cell pair are equivalent to it. This is repeated at each level of movement away from the initial pair because there will always be an even number of cells between the members of each new pair of cells. The mean value of the range of all of the rows is n2 - n. 1 - 2x, where x is the value of the seed cell.
All rows are magical.
Therefore, each row must be magical. This follows directly from Observation 6 and the fact that there are n cells in every row. The median values of each row appear in the cell pair congruent to and farthest from the seed column's cell pair, or what might be called the row's mirror-seed column's cell pair. This follows directly from the construction algorithm and the definition of congruent cell pairs. The median values of the square appear in the bottom row's mirror-seed column cell pair.