Define the sign of a permutation $ to be:
sgn $ = 1 if $ is even. -1 if $ is odd.
Prove that sgn($%) = sgn$sgn% for all $ and % in Sn.
We know each permutation can be expressed as the products of 2-cycles. 2-cycle is the form of (ab). If a permutation has odd ...
A proof involving the signs of permutations is provided. The proof is concise.