Using permute function for rearrange or for transpose complex multi-dim arrays. Do I need to conj before?

Hello

Please help me to understand: I figured out that for doing transpose of a complex multi-dim array (3d or 4d ...) I need to conjugate my array before, like:

permute(conj(A),[2 1 3]);

Am I right?

But then if I need only to rearrange the dimensions of my complex array (like 4th dimension will be 3rd) ,

Bnew = permute((B),[1 2 4 3]);

do I need to conjugate my array also?

I get confused, because later if do:

permute((Bnew),[1 2 4 3]);

I will get the same array as B, right?

Thank you!