proposition: Lemma matrix_inverse_to_right_and_left_inverse {n : nat} (A : Matrix R n n) : (matrix_inverse A) -> matrix_left_inverse A × matrix_right_inverse A.
proof: Proof. intros inv; split. - apply matrix_left_inverse_of_inverse; exact inv. - apply matrix_right_inverse_of_inverse; exact inv. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Vectors UniMath.Algebra.RigsAndRings UniMath.Algebra.IteratedBinaryOperations UniMath.Algebra.Matrix UniMath.Algebra.Domains_and_Fields UniMath.Algebra.GaussianElimination.Auxiliary UniMath.Algebra.GaussianElimination.Vectors