∀ (R : Type u_2) {ι : Type u_1} [inst : Ring R] [inst_1 : Fintype ι] [inst_2 : DecidableEq ι]
  (M : ModuleCat (Matrix ι ι R)) (j : ι) (x : Matrix ι ι R) (m : ↑M),
  (fun i => ⟨Matrix.single j i 1 • x • m, ⋯⟩) = (RingHom.id (Matrix ι ι R)) x • fun i => ⟨Matrix.single j i 1 • m, ⋯⟩