Let , where , be an affine general linear group of degree 2 over the field of order 3. It is the external semidirect product of the vector space by by linear transformations.
Since the action of is natural on , we have , where . See here.
The matrix representation of is as follows:
where M is an matrix over K and v is an column vector.
I think the number of non-isomorphic faithful matrix representations of and the corresponding special affine general linear group are the orders of and , where (see here to find the order of general linear group over a finite field).