Looks great! I don't think you can do anything more, unless you happen to know before-hand that C is unitary.
Given that A, B and C are invertible n x n matrices, simplify
First I expanded to :
Then I found the inverse of the matricies within the parenthesis:
and are just I (the identity matrix) and can be removed:
Does this look correct? My text has no solution for this question. I'm trying to think if I can do something with the C matrices.