Let G denote the group of all 2x2 real matrices with non-zero determinants. Let H denote...

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Let G denote the group of all 2x2 real matrices with non-zero determinants. Let H denote the subgroup of all matrices with determinant 1. Let denote the set of left cosets of H. Then H is normal subgroup G is isomorphic to the real numbers under addition H is isomorphic to the non-zero real numbers under multiplication. H is a infinite order non-cyclic group. H Let G denote the group of all 2x2 real matrices with non-zero determinants. Let H denote the subgroup of all matrices with determinant 1. Let denote the set of left cosets of H. Then H is normal subgroup G is isomorphic to the real numbers under addition H is isomorphic to the non-zero real numbers under multiplication. H is a infinite order non-cyclic group. H

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