22. Prove that the set = {(₁ ~ ) 1} x) | : x, y ≤ R, x² + y² = 1 = SO(2) = forms an abelian group with respect to multiplication.
22. Prove that the set = {(₁ ~ ) 1} x) | : x, y ≤ R, x² + y² = 1 = SO(2) = forms an abelian group with respect to multiplication.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
. Prove that the set
S0(2) = { : z,y }
forms an abelian group with respect to multiplication.
![22. Prove that the set
{(;?)
x -y
SO(2) =
:x, y € R, x² + y° = 1}
forms an abelian group with respect to multiplication.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e130045-f67e-4ba8-bac2-94143c4c0cb7%2Febc80eda-a556-46a2-9fc3-2291ffbe0901%2Fck8o78f_processed.png&w=3840&q=75)
Transcribed Image Text:22. Prove that the set
{(;?)
x -y
SO(2) =
:x, y € R, x² + y° = 1}
forms an abelian group with respect to multiplication.
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