Consider a matrix $$ A= \begin{pmatrix} a_{11} & a_{12} & a_{13} & a_{14} & a_{15} & a_{16} \\ a_{21} & a_{22} & a_{23} & a_{24} & a_{25} & a_{26} \end{pmatrix}, $$ in which sum of the elements of each colon is zero and $a_{i,j}=\pm1$. Suppose also that $E(A)=C$.
Define sub-matrices $A_1=\begin{pmatrix} a_{11} & a_{12}\\ a_{21} & a_{22} \end{pmatrix}$, $A_2=\begin{pmatrix} & a_{13} & a_{14}\\ & a_{23} & a_{24} \end{pmatrix}$, $A_3=\begin{pmatrix} & a_{15} & a_{16} \\ & a_{25} & a_{26} \end{pmatrix}$. Is it possible to represent expectations of $A_1, A_2, A_3$ through $E(A)=C$?