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Ok = (6) Let n be a positive integer. For every integer k, define the 2...

Ok = (6) Let n be a positive integer. For every integer k, define the 2 x 2 matrix cos(27k/n) - sin(2nk/n) sin(2tk/n) cos(27

Ok = (6) Let n be a positive integer. For every integer k, define the 2 x 2 matrix cos(27k/n) - sin(2nk/n) sin(2tk/n) cos(27 k/n) (a) Prove that go = I, that ok + oe for 0 < k < l< n - 1, and that Ok = Okun for all integers k. (b) Let o = 01. Prove that ok ok for all integers k. (c) Prove that {1,0,0%,...,ON-1} is a finite abelian group of order n.
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For every cos (24) sin (27/n) sin (21Tk/n) co8 (21 km) (oso -sino I2x2 () sino COSO for osKLI sn-1 in I # QITK let if possibl- kth 11 Los (211 + 2Tk 27K) - sin (211 + 21114) sin (21+ 274) Cos (21T+ ztic n Cos (211+0) = Coso, sin (utto) -sino. los 2TRfrom 6 6 . &KEY rk бр Ion from q on a Soth = = I on 18 ordern. { I, 6, 62, ..., ght? a cyclic group of = 1 { 1, 6, 83, ..., g

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