### Sage is not returning all solutions to equations modulo n

I am trying to find all 2x2 matrices S over ~~Z/9Z ~~$Z/9Z$ such that ~~S^3=I, ~~$S^3=I$, where I is the identity matrix. I am currently using the following ~~procedure:
~~procedure:

```
S = matrix(SR, 2, [[a,b],[c,d]]);S3=S^3
l=solve_mod([S3[0,0]==1,S3[0,1]==0,S3[1,0]==0,S3[1,1]==1],
```~~9);l~~9);l

The list of solutions (there are 207) I receive does not include ~~S=[[1,3],[3,1]], ~~`S=[[1,3],[3,1]]`

, for example, which does in fact satisfy ~~S^3=I. ~~$S^3=I$. I am new to Sage, is there something I am missing? How can I get a complete list of solutions?