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Single-line solution:

[M.change_ring(ZZ) for s in GL(GF(2),2) if not (M:=Matrix(s)).is_symmetric()]

Single-line solution:

[M.change_ring(ZZ) for s in GL(GF(2),2) GL(2,GF(2)) if not (M:=Matrix(s)).is_symmetric()]

Single-line solution:

[M.change_ring(ZZ) for s v in GL(2,GF(2)) Tuples((0,1),4) if not (M:=Matrix(s)).is_symmetric()]
(M:=Matrix(2,2,v)).is_symmetric()]

Single-line solution:

[M.change_ring(ZZ) [M for v in Tuples((0,1),4) if not (M:=Matrix(2,2,v)).is_symmetric()]

Single-line solution:

W = [M for v in Tuples((0,1),4) if not (M:=Matrix(2,2,v)).is_symmetric()]