Question

(a+b) ^-1×(a^-1+b^-1) = a^x b^y find x+y+2

Answer 1

Answer:4

I'm trying to prove the below equation, where a,b∈G and (G,∗) is a group.

(a∗b)−1=(a−1)∗(b−1)

I'm not really sure how to do it though. I tried doing something like

(a∗b)−1∗(a∗b)=e=a∗a−1∗b−1∗b

(a∗b)−1∗(a∗b)=e=a∗(a−1∗b−1)∗b

However, I can't get the RHS to (a∗b)∗(a−1∗b−1) without assuming communitivity.

How would I go about doing this? Any help is appreciated.

Thanks

Edit: Given that correction, would this be correct?

(a∗b)−1∗(a∗b)=e=a∗(b∗b−1)∗a−1

Then

a∗(b∗b−1)∗a−1=a∗b∗(b−1∗a−1)=(a∗b)∗(b−1∗a−1)

Thus

(a∗b)−1=(b−1∗a−1)

Answer 2

hope this helps uh dear❤❤❤❤❤☹