[Tex/LaTex] Making size of a 4×4 matrix that consist only 2 parameter of 2×2 matrix to be same size as 4×4 matrix

#enumeratematricesmulticol

From the picture below, both are supposed to be 4×4 matrices, but I want to express the first one with 2×2 matrix within 2×2 matrix where the J1 and J2 are 2×2 matrices while the 0 is 2×2 zero matrix. I wanted to make the size to look the same as this looks somehow ugly. Anyone has idea? I attached the code as well. 

\begin{multicols}{2}
\begin{enumerate}
    \item $\begin{Bmatrix}
    J_1 & 0 \\
    0 & J_2 
    \end{Bmatrix}$
    \item $\begin{Bmatrix}
        \lambda_0 & 1 & 0 & 0 \\
        0 & \lambda_0 & 1 & 0 \\
        0 & 0 & \lambda_0 & 0 \\
        0 & 0 & 0 & \lambda_1
        \end{Bmatrix}$ 
    \item $\begin{Bmatrix}
            \lambda_0 & 1 & 0 & 0 \\
            0 & \lambda_0 & 1 & 0 \\
            0 & 0 & \lambda_0 & 1 \\
            0 & 0 & 0 & \lambda_0
            \end{Bmatrix}$ 
    \item $\begin{Bmatrix}
            \alpha & \beta & 1 & 0 \\
            -\beta & \alpha & 0 & 1 \\
            0 & 0 & \alpha & \beta \\
            0 & 0 & -\beta & \alpha 
            \end{Bmatrix}$
\end{enumerate}
\end{multicols}

enter image description here

Best Answer

enter image description here

\documentclass{article}
\usepackage{multicol,amsmath}

\begin{document}
\begin{multicols}{2}
\begin{enumerate}
    \item $\begin{Bmatrix}
\begin{picture}(0,0)\put(5,-8){\boldmath\large$J_1 $}\end{picture}
&&
\begin{picture}(0,0)\put(5,-8){\boldmath\large$0$}\end{picture}
&\\
\phantom{\lambda_1}&
\phantom{\lambda_1}&
\phantom{\lambda_1}&
\phantom{\lambda_1}\\
\begin{picture}(0,0)\put(5,-8){\boldmath\large$0$}\end{picture}
 &&
\begin{picture}(0,0)\put(5,-8){\boldmath\large$J_2 $}\end{picture}
&\\
\phantom{0}
    \end{Bmatrix}$
    \item $\begin{Bmatrix}
        \lambda_0 & 1 & 0 & 0 \\
        0 & \lambda_0 & 1 & 0 \\
        0 & 0 & \lambda_0 & 0 \\
        0 & 0 & 0 & \lambda_1
        \end{Bmatrix}$ 
    \item $\begin{Bmatrix}
            \lambda_0 & 1 & 0 & 0 \\
            0 & \lambda_0 & 1 & 0 \\
            0 & 0 & \lambda_0 & 1 \\
            0 & 0 & 0 & \lambda_0
            \end{Bmatrix}$ 
    \item $\begin{Bmatrix}
            \alpha & \beta & 1 & 0 \\
            -\beta & \alpha & 0 & 1 \\
            0 & 0 & \alpha & \beta \\
            0 & 0 & -\beta & \alpha 
            \end{Bmatrix}$
\end{enumerate}
\end{multicols}
\end{document}
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