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Let G = GL(2, R) and let K be a subgroup of R*. Prove that

Chapter 9, Problem 7E

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QUESTION:

Let \(G=G L(2, \mathbf{R})\) and let K be a subgroup of \(\mathbf{R}^*\). Prove that \(H=\{A \in G \mid \operatorname{det} A \in K\}\) is a normal subgroup of G.

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QUESTION:

Let \(G=G L(2, \mathbf{R})\) and let K be a subgroup of \(\mathbf{R}^*\). Prove that \(H=\{A \in G \mid \operatorname{det} A \in K\}\) is a normal subgroup of G.

ANSWER:

Step 1 of 2

Let and let K be a subgroup of. To prove  is a normal subgroup, defined as follows

Let, consider the group  

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