Question

suppose that a,b are elements of a group and a^5=e, b^4=e, ab=ba^3
Prove that (i) a^b =ba (ii) ab^3=b^3a^2

Answer 1

you sure there are no typos, for part a) a^b = ba ?

Answer 2

so this is like a puzzle

Answer 3

apply multiplication on both sides

Answer 4

dont understand

Answer 5

ab=ba^3

multiply both sides by a^2 (on the right)
ab *a^2 = b*a^3 * a^2

aba^2 = b* a^5
aba^2 = b*e
aba^2 = b

Answer 6

ab=ba^3
multiply both sides by a^2 (on the right)
ab *a^2 = b*a^3 * a^2
ab*a^2 = b* a^5
aba^2 = b*e
aba^2 = b

Answer 7

i think you can make a table

Answer 8

i will be able to answer more quickly if i see the original worksheet or problem

Answer 9

can you take a picture of the question and upload it?

Answer 10

i cant it was written down on a piece of paper