$\langle A,B\rangle = \operatorname{tr}(B^*A)$ "define the inner product of two matrices $A$ and $B$ in $M_{n\times n}(F)$ by $$\langle A,B \rangle = \operatorname{tr}(B^*A), $$ where the {conjugate transpose} (or {adjoint}) $B^*$ of a matrix $B$ is defined by $B^*_{ij} = \overline{B_{ji}}.$
Prove that $\langle B,A \rangle = \overline{\langle A,B \rangle}$
This is left to the reader in my linear algebra text book and can't seem to work out a solution. Any help would be much appreciated.  

Hint: $\operatorname{tr}(AB)=\operatorname{tr}(BA)$.
