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Let G be the subgroup of invertible matrices generated by A = 2 1 ( 1 1 1 1 ) and B = ( 1

Let G be the subgroup of invertible matrices generated by A=21(1111) and

B=(1001).

  1. Let H be the cyclic subgroup generated by C=AB. Determine the order of H.
  2. Show that HG.
  3. Compute the order of G/H and deduce G.

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