Question

Prove that if you compose two even permutations, you get an even permutation.

Answer 1

even+even=even

Answer 2

permutation formula nPr = n!/(n-r)!
where n is total object taken, and
r= objects taken at a time

proof:
nPr =n!/(n-r)!
2P2= 2!/(2-2)!
= 2!/0!
= 2
where 2 is even

Answer 3

therefore, if you compose two even permutation you'll always get an even answer

Answer 4

try other given like 4P2 and you will also get an even answer.

Answer 5

I think what he meant by even permutation are the elements in permutation group that can be written as a product of even cycles.

Answer 6

Sorry back, ye what watchmath said, logically it makes sense since you need a even number of transpositions to compose a even permutation, but i wasn't sure of the generic proof.