The two-dimensional space
contains nine points: (0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,1), and (2,2). The 48 invertible 2×2 matrices over
form the general linear group known as
. They act on
by matrix multiplication modulo 3, permuting the nine points. More generally,
is the set of invertible
matrices over the field
With (0,0) shifted to the center, the matrix actions on the nine points make symmetrical patterns.