Answer to Question #300236 in Abstract Algebra for ksmoorthy

Question #300236

Find aba -1


where (i) a = (5 , 7 , 9) , b = (1 , 2, 3) (ii) a = (1 , 2,5)(3 , 4) , b = (1 , 4 , 5) .

1
Expert's answer
2022-02-22T03:20:39-0500

Let us find "aba^{-1}" where

(i) "a=(5,7,9),\\ b=(1,2,3)"


It follows that "a^{-1}=(5,9,7)." Taking into account that the circles "a" and "b" are independent, and hence they commute, we conclude that

"aba^{-1}=(5,7,9) (1,2,3)(5,9,7)=(1,2,3)(5,7,9)(5,9,7)=(1,2,3)=b."



(ii) "a=(1,2,5)(3,4),\\ b =(1,4,5)"


It follows that "a^{-1}=(3,4)(1,5,2)." Therefore,

"aba^{-1}=((1,2,5)(3,4))(1,4,5)((3,4)(1,5,2))=((134)(2,5))((3,4)(1,5,2))\n=(123)."



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS