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