  In dRGT massive gravity, to get the equations of motion, the square root
tensor is assumed to be invertible in the variation of the action. However,
this condition can not be fulfilled when the reference metric is degenerate.
This implies that the resulting equations of motion might be different from the
case where the reference metric has full rank. In this paper, by generalizing
the Moore-Penrose inverse to the symmetric tensor on Lorentz manifolds, we get
the equations of motion of the theory with degenerate reference metric. It is
found that the equations of motion are a little bit different from those in the
non-degenerate cases. Based on the result of the equations of motion, for the
$(2+n)$-dimensional solutions with the symmetry of $n$-dimensional maximally
symmetric space, we prove a generalized Birkhoff theorem in the case where the
degenerate reference metric has rank $n$, i.e., we show that the solutions must
be Schwarzschild-type or Nariai-Bertotti-Robinson-type under the assumptions.
