1. Let T be a group of all invertible 2 x2 matrices of the form Where a.b.C ER and ac+0. Let / be the set of matrices of the form 0 1 where x ER. a. Prove that U is a subgroup of T. b. Determine whether U is a normal subgroup of T. 2. Let G be a group. Prove or disprove that z= {XE G: xg = gx for all ge G} is a Subgroup of G .

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