Group Theory: Group example of GL2,R, SL2,R Quaternion

Group Theory: Definition and examples of GL(2,R), SL(2,R)
|| Quaternion group ||
The result of inverse of elements and elements having same order
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[@user-gs1ci3tm9j]

Thanks you help me well

[@alancristopher3539]

How Prove that GL(2,R)/SL(2,R) is isomorphic to R* ?

[@mahimudhiraj158]

Inverse of 3 is 5...how we will know mam?

[@MathematicsFreak]

This is a group for multiplication so take 3*1=3,3*2=6,3*3=9,3*4=12,3*5=15...now apply modulo 7 now elements will be 9/7=2,12/7=5,15/7=1....a*a^-1=identity=1(multiplication)

[@MrChicken1joe]

How is the first example an example for Sl(2,R) if Z5 isnt even a subset of R? Because Z5 consists of elements that are Sets of Integers, right? Isnt this a contradiction to the definition of Sl(2,R)?

[@MathematicsFreak]

Actually symbol of special type matrix is SL(2,F) ......or R,Q,C,Zp are field so entries of special type matrix are also belonging from R,Zp...

[@MathematicsFreak]

I hope you are getting my point