gap> mat := [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,-1]]*Z(9)^0;
[ [ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ], 
  [ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3) ] ]
gap> form := BilinearFormByMatrix(mat,GF(9));
&lt; bilinear form >
gap> Display(form);
Bilinear form
Gram Matrix:
 1 . . .
 . 1 . .
 . . 1 .
 . . . 2
gap> IsReflexiveForm(form);
true
gap> IsSymmetricForm(form);
true
gap> IsAlternatingForm(form);
false
gap> r := RadicalOfForm(form);
&lt;vector space over GF(3^2), with 0 generators>
gap> Dimension(r);
0