gap> mat := [[1,0,2,0],[0,2,0,1],[2,0,0,0],[0,1,0,0]]*Z(9)^0;
[ [ Z(3)^0, 0*Z(3), Z(3), 0*Z(3) ], [ 0*Z(3), Z(3), 0*Z(3), Z(3)^0 ],
[ Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ] ]
gap> phi := PolarityOfProjectiveSpace(mat,GF(9));
<polarity of PG(3, GF(3^2)), >
gap> IsOrthogonalPolarityOfProjectiveSpace(phi);
true