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.