Find the cyclic subgroup generated by
2 1
0 2
(matrix)
in .
I suppose im confused as to what exactly it's asking me to do. signifies 2x2 matrices with mod3 entried, correct? How do I find the cyclic subgroup?
The cyclic subgroup generated by the element is all elements of the form for . So, just find , , , etc until you get back to the identity. The powers of your generator will be your group.