∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] (e : M ≃ₗ[R] M)
  (f f' : M →ₗ[R] M), (∀ (x : M), f x = f' (e x)) → Associated (LinearMap.det f) (LinearMap.det f')