Since the determinant is a multiplicative function - det(MN)=det(M)det(N) - we can observe the the determinant is a homomorphism from the group of permutation matrices to the group \(\{\pm ...Since the determinant is a multiplicative function - det(MN)=det(M)det(N) - we can observe the the determinant is a homomorphism from the group of permutation matrices to the group {±1}. Demostrar que cada una de las tres definiciones del signo de una permutación dan un homomorfismo deSn to {1,−1}. (For the third definition, a sketch of a proof will suffice.
