representing of expectation for submatrices

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 $E(A)=C$?