Let G = GL2(R). Prove that each of the following subsets is a subgroup of G. {[: a (а) Н a, b e R, a # 0 0 а-1 (b) K = {A € G| det(A) E {±1}}. 1 1 1 0 1 1 A (c) L =

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Q: Exercise 5.1.10. Let HC G. Show that H is a subgroup of G if and only if H is non-empty and for all…

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Q: Let G = GL2(R). {[ {[ а (a) Prove that T = | a, c, d e R, ad is a subgroup of G. d a (b) Prove that…

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Q: Let C2 = {±1} be a subgroup of R". Prove that R = R+ x C2 where R is the set of real numbers.

A: Please check step 2 and 3 for the solution.!

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Q: Question 10. Prove in detail that G(T) is a subgroup of G.

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Q: 6. Show that the special orthogonal group is compact. SO(n) := {A = O(n)| det A = 1}

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