I am given that $A^{-1,T} = A^{T,{-1}}$, and I have to prove that $A^{-1,\dagger} = A^{\dagger,{-1}}$. I tried representing the question as
$$A^{-1,{T*}} = A^{T*,{-1}}$$
$$A^{T,{-1*}} = A^{T*,{-1}}$$
but I still can't figure out how to prove that the complex conjugate can commute. Am I allowed to assume it can or do I need to be more specific?
$AA^{-1}=I$
$A^{-1, \dagger}A^{\dagger} = I^{\dagger} = I$
It follows $A^{-1, \dagger}$ is the inverse of $A^{\dagger}$
ie $A^{\dagger, -1} = A^{-1, \dagger}$
Line 2 uses the property $(BC)^{\dagger} = C^{\dagger}B^{\dagger}$