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.
Doing algebra without the normal commuting rules is super unintuitive for me. Did I do this right?
"If G is a group and , write in terms of and "
What I did (I'm doing all of my operations on the right hand side):
Is that right? It seems weird to me that splitting the h and g would make them switch places.