Show that the set of six transformations f1, f2, f3, f4, f5, f6 on the set of complex numbers defined by f (z) z 1 , zf z 1 ( ) 2 , f (z) 1 z 3 , 1 ( ) 4 z z f z , z f z 1 1 ( ) 5 , zz f z1( ) 6 forms a finite non-abelian group of order six with respect to the composition known as composite of two functions or product of two functions
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