From those thoughts it can immediately be concluded, that a pandiagonal square, that is split between two rows or two columns and those parts are exchanged, is pandiagonal again. In the illustration the two top rows are detached and attached at the bottom end of the square. The resulting square is also pandiagonal.
In the illustration above the left two columns are detached and attached at the right end of the square. The resulting square is pandiagonal, too.
Expressed differently: Every horizontal or vertical translocation in any direction again results in a pandiagonal square, if the rows and columns are seen cyclic.
In the illustration above the cell (3/4) ist made the upper left corner through translocation. Because of the cyclic arrangement of the square also this translocation results in a pandiagonal square.