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
, where
is prime
With (0,0) shifted to the center, the matrix actions on the nine points make symmetrical patterns.
