  We derive exact inversion identities satisfied by the transfer matrix of
inhomogeneous interaction-round-a-face (IRF) models with arbitrary boundary
conditions using the underlying integrable structure and crossing properties of
the local Boltzmann weights. For the critical restricted solid-on-solid (RSOS)
models these identities together with some information on the analytical
properties of the transfer matrix determine the spectrum completely and allow
to derive the Bethe equations for both periodic and general open boundary
conditions.
