Determinant_with_Rows_Transposed_v3

import Mathlib.LinearAlgebra.Matrix.Determinant.Basic

theorem Determinant_with_Rows_Transposed_v3 {R : Type _} [CommRing R] {n : ℕ} (A : Matrix (Fin n) (Fin n) R) (i j : Fin n) (hij : i ≠ j) : (A.submatrix (Equiv.swap i j) id).det = -A.det := by sorry