We defined the operation $ \Delta $ as
$ (a,b) \Delta (c,d) = (ac + \delta bd, ad + bc) $ where $ a, b, c ,d \in \mathbb{Q} $
I have already proven that this operation is both commutative and associative.
I have also found it's identity element which is $ (1,0) $.
I am now asked to find it's inverse.
How would I approach this? Thanks !
To find the inverse in a vector space,by definition,this means:
$ (a,b) \Delta (c,d) = (ac + \delta bd, ad + bc)=(1,0)$ where $ a, b, c ,d \in \mathbb{Q} $
So : $ac + \delta bd = 1 $ $ad + bc = 0$
We have to solve for c and d in the system. So solve the system. You should be able to do the rest yourself now.