 BRST-invariant operators are operators for which ["Q", "A") = 0.Since the operators are also graded by ghost numbers, this BRST transformation also forms a cohomology for the operators since ["Q", ["Q", "A")) = 0.Although the BRST formalism is more general than the Faddeev-Popov gauge fixing, in the special case where it is derived from it, the BRST operator is also useful to obtain the right Jacobian associated with constraints that gauge-fix the symmetry.