Matrix representation of a group

[VINAYBAR]

I am unable to grasp how to generalise the concept of matrix representation for a group say like D3 or D4.I know how to manipulate the 2x2 matrix,but how do I obtain a group in say a 3x3 matrix to show rotation and reflection?

 

[closet mathemetician]

This paper has a very accessible treatment of groups and their representations as matrices. The author uses the group S3 as an example.
http://arxiv.org/abs/0810.3328"