
EXAMPLE

From Petros Hadjicostas, Dec 18 2019: (Start)
For n = 2, the 4*a(2) = 64 n X n matrices M with elements in 0..7 that satisfy MM' mod 8 = I can be classified into four categories:
(a) Matrices M with 1 = det(M) mod 8. These form the abelian group SO(2, Z_8). See the comments for sequence A060968.
(b) Matrices M with 3 = det(M) mod 8. These are the elements of the left coset A*SO(2, Z_8) = {AM: M in SO(2, Z_8)}, where A = [[3,0],[0,1]].
(c) Matrices M with 5 = det(M) mod 8. These are the elements of the left coset B*SO(2, Z_8) = {BM: M in SO(2, Z_8)}, where B = [[5,0],[0,1]].
(d) Matrices M with 7 = det(M) mod 8. These are the elements of the left coset C*SO(2, Z_8) = {CM: M in SO(2, Z_8)}, where C= [[7,0],[0,1]].
All four classes of matrices have the same number of elements, that is, 16 each.
Note that for n = 3 we have 4*a(3) = 4*1536 = 6144 = A264083(8). (End)
