  Dunfield-Garoufalidis and Boyer-Zhang proved that the A-polynomial of a
nontrivial knot in $S^{3}$ is nontrivial. In this paper, we use holonomy
perturbations to prove the non-triviality of the A-polynomial for a nontrivial,
null-homotopic knot in an irreducible 3-manifold. Also, we give a strong
constraint on the A-polynomial of a knot in the 3-sphere.
