∀ {R : Type u_1} {m : Type u_2} {n₁ : Type u_6} {n₂ : Type u_7} (A₁ : Matrix m n₁ R) (A₂ : Matrix m n₂ R)
  (B₁ : Matrix m n₁ R) (B₂ : Matrix m n₂ R), A₁.fromCols A₂ = B₁.fromCols B₂ ↔ A₁ = B₁ ∧ A₂ = B₂