Example of a finite vector space

The vector space of dimension 2 over the finite field GF(3) is isomorphic to the abelian group Z3 X Z3.

gap> b:=One(GF(3))*[[1,0],[0,1]];
[ [ Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3)^0 ] ]
gap> V:=VectorSpace(GF(3),b);

gap> Dimension(V);
2
gap> Size(V);
9
gap> Elements(V);
[ 
[ 0*Z(3), 0*Z(3) ], 
[ 0*Z(3), Z(3)^0 ], 
[ 0*Z(3), Z(3) ], 
[ Z(3)^0, 0*Z(3) ],
[ Z(3)^0, Z(3)^0 ], 
[ Z(3)^0, Z(3) ], 
[ Z(3), 0*Z(3) ], 
[ Z(3), Z(3)^0 ], 
[ Z(3), Z(3) ] 
]