If $A(z) :=[A_{ij}(z)] $ and $B(z) :=[B_{ij}(z)] $  are two $n\times n$ matrices of entire complex valued functions entries $A_{ij}(z)$, and $B_{ij}(z) $ with 

(1). $AA^{\#}=A^{\#}A$  where $A^{\#}(z)=\left(\overline{A(\bar{z})} \right)^{T}$.

(2). $BB^{\#}=B^{\#}B$ 

(3).$ AB=BA$

 Is it true that 
$$B(A A^{\#}) =(AA^{\#}) B$$. 

Thanks in advance.