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Conjugate if symmetric in Cayley table

Show that for x,y elements of G are conjugate if they appear symmetrically across the diagonal in the Cayley table of G.

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Elements x and y appearing across the diagonal in the Cayley table of G mean there are some elements a and b of G such that x = a*b and y = b*a.

Definition of conjugate:
Elements x and y of group G ...

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