I have a problem that states(adsbygoogle = window.adsbygoogle || []).push({});

Define the Special linear group by: (Let R denote real numbers)

[tex]SL(2,R) = \{ A\in GL(2,R): det(A)=1\}[/tex]

Prove that SL(2,R) is a subgroup of GL(2,R).

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Now a subset H of a group G is a subgroup if:

i) [tex]1 \in H[/tex]

ii) if [tex] x,y \in H[/tex], then [tex]xy \in H[/tex]

iii) if [tex]if x\in H[/tex], then [tex]x^{-1} \in H[/tex]

I have very little knowledge of matricies and I don't even see how 1 could be in SL(2,R), other than maybe something saying that GL(2,R) has 1, so SL(2,R) must have it too, but I bet there is a more appropriate way.

Also what would H be here? Would it a set containing matricies or numbers?

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# Linear Groups

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