The primitive unit cell for this structure is (2 x 2)R45
The primitive unit cell is again illustrated below - the cell is square in shape but has sides which are longer than those of the substrate unit cell by a factor of 2 (i.e. |b1| = 2|a1| and |b2| = 2|a2|) and is also rotated by 45 degrees with respect to the substrate cell.
It is therefore a (2 x 2)R45 structure.
What is the matrix description for this structure ?
(Remember that the matrix method always describes the primitive unit cell)