∀ {m : Type u_2} {R : Type u_4} {α : Type u_3} {β : Type u_1} [inst : Fintype m] [inst_1 : DecidableEq m]
  [inst_2 : CommSemiring R] [inst_3 : Semiring α] [inst_4 : Semiring β] [inst_5 : Algebra R α] [inst_6 : Algebra R β]
  (f : α →ₐ[R] β) (r : R), ((algebraMap R (Matrix m m α)) r).map ⇑f = (algebraMap R (Matrix m m β)) r