Answer to Question #300208 in Abstract Algebra for ksmoorthy

Question

F ind aba -1 w here (i) a = (5 , 7 , 9) , b = (1 , 2, 3) (ii) a = (1 , 2,5)(3 , 4) , b = (1 , 4 , 5) .

Answer 1

Solution:

$aba^{-1}=(ab)a^{-1} \\=(ba)a^{-1} \\=baa^{-1} \\=b(aa^{-1}) \\=b(1) \\=b$

(i):

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

$aba^{-1}=b=(1,2,3)$

(ii):

a = (1 , 2,5)(3 , 4) , b = (1 , 4 , 5)

$aba^{-1}=b=(1,4,5)$