gap> mat := IdentityMat(4,GF(16));
[ [ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ] ]
gap> phi := HermitianPolarityOfProjectiveSpace(mat,GF(16));
<polarity of PG(3, GF(2^4)), >
gap> geom := GeometryOfAbsolutePoints(phi);
<polar space over GF(2^4)>
gap> mat := [[1,0,0,0],[0,0,1,1],[0,1,1,0],[0,1,0,0]]*Z(32)^0;
[ [ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ],
[ 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ] ]
gap> phi := PolarityOfProjectiveSpace(mat,GF(32));
<polarity of PG(3, GF(2^5)), >
gap> geom := GeometryOfAbsolutePoints(phi);
<a plane in ProjectiveSpace(3, 32)>