$A=\left[
\begin{array}{cc}
0 & 1 \\
1 & 0 \\
\end{array}
\right]<==>\left[\begin{array}{cccc}
0 & 0 & 1 & 1 \\
0 & 0 & 1 & 1 \\
1 & 1 & 0 & 0 \\
1 & 1 & 0 & 0 \\
\end{array}\right]=A^{'}$
$B=\left[
\begin{array}{ccc}
0 & 1 & 1 \\
1 & 0 & 0 \\
1 & 0 & 0 \\
\end{array}
\right]<===>\left[
\begin{array}{cccccc}
0 & 0 & 1 & 1 & 1 & 1 \\
0 & 0 & 1 & 1 & 1 & 1 \\
1 & 1 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 0 & 0 \\
\end{array}
\right]=B^{'}$
From the above we can obtain the RHS matrices from LHS by replacing $k\times k$ block submatrices in the corresponding entries of A. Here, in the above example $k=2$. Here My question is how to denote RHS matrix in terms of LHS in general?
Let $E_k$ denote the $k\times k$-matrix with entries only $1$, hence $$ E_k = \begin{pmatrix} 1 & \cdots & 1 \\ \vdots & \ddots & \vdots \\ 1 & \cdots & 1 \end{pmatrix} $$ Then, with $\otimes$ denoting the Kronecker product, we have $$ A' = A \otimes E_2, B' = B \otimes E_2 $$