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## Homework Statement

Let a and b be elements of a group,with a^2=e , b^6=e and a.b=b^4.a find its order and express its inverse in form of a^m.b^n

## Homework Equations

## The Attempt at a Solution

(ab)^2=(ab)(ab)=(ab)(b^4.a)=a(b^5)a

(ab)^3=a(b^5)a(ab)=a(b^5)(a^2)b=a(b^6)=ae=a

it implies(ab)^6=e

thus order(ab) divides 6.It is not 3 hence it is 6.

Help me in solving second part.I can express inverse in form of b^m.a^n but not in the asked form.