  We study a recent proposed Ricci-inverse gravity, which is a very novel type
of fourth-order gravity. In particular, we are able to figure out both
isotropically and anisotropically inflating universes to this model. More
interestingly, these solutions are free from a singularity problem. However,
stability analysis based on the dynamical system method shows that both
isotropic and anisotropic inflation of this model turn out to be unstable
against field perturbations. This result implies a no-go theorem for both
isotropic and anisotropic inflation in the Ricci-inverse gravity.
