Is my non-commutative algebra correct?
Doing algebra without the normal commuting rules is super unintuitive for me. Did I do this right?
"If G is a group and 
, write ^{-1})
in terms of 
and 
"
What I did (I'm doing all of my operations on the right hand side):
^{-1}(gh)=e)
^{-1}(ghh^{-1})=h^{-1})
^{-1}(gg^{-1})=h^{-1}g^{-1})
^{-1}=h^{-1}g^{-1})
Is that right? It seems weird to me that splitting the h and g would make them switch places.
Re: Is my non-commutative algebra correct?
your algebra is correct. you can think of it this way:
when you take off your shoes and socks, you do it in the opposite order as you put them on.
Re: Is my non-commutative algebra correct?
Thanks!
Ick, that tex was awful. My bad.
