∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Free R M]
  [Module.Finite R M] (A : Type u_3) [inst_5 : CommRing A] [inst_6 : Algebra R A] (f : M ≃ₗ[R] M),
  LinearEquiv.det (LinearEquiv.baseChange R A M M f) = (Units.map ↑(algebraMap R A)) (LinearEquiv.det f)