More generally, is the set of invertible matrices over the field With shifted to the center, the matrix actions on the points make symmetrical patterns.

The controls let you choose a modulus, which then computes the size of the group. A 3×3 matrix can then be chosen. If the determinant is zero or the determinant and modulus share a factor, the matrix is not invertible and thus not in the group. The chances of being in the group are roughly

The matrix and its inverse (if it exists) are shown, along with their determinants. Finally, a grid of the loops is shown.