Thread: Permutation

Show that if pi and sigma are permutations such that (pi*sigma)^2 =(pi^2)(sigma^2) then (pi*sigma)=(sigma*pi)

Originally Posted by r7iris

Show that if pi and sigma are permutations such that (pi*sigma)^2 =(pi^2)(sigma^2) then (pi*sigma)=(sigma*pi)

Just expand.

$(ab)^2 = a^2b^2$
$abab=aabb$
$ab=ba$

Originally Posted by r7iris

Show that if pi and sigma are permutations such that (pi*sigma)^2 =(pi^2)(sigma^2) then (pi*sigma)=(sigma*pi)

Simple. We know the inverse permutations (on the left and right) exist, so:












-Dan