[Tex/LaTex] How to write code for the following matrix

Question

Can you help me to write code for the following matrix…
I have done one part of the code:

\begin{displaymath}
\begin{pmatrix}
a_{11} & a_{12} & a_{13} \\
a_{12} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{pmatrix}=
\begin{pmatrix}
\end{pmatrix}
\end{displaymath}

Answer 1

You can nest the matrix environment:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
    \begin{equation}
        \mathop{\mathbf{adj}}
        \begin{pmatrix}
            a_{11} & a_{12} & a_{13} \\
            a_{12} & a_{22} & a_{23} \\
            a_{31} & a_{32} & a_{33}
        \end{pmatrix}
        =
        \begin{pmatrix}
            +
            \begin{vmatrix}
                a_{22} & a_{23} \\
                a_{32} & a_{33}
            \end{vmatrix} &
            -
            \begin{vmatrix}
                a_{12} & a_{13} \\
                a_{32} & a_{33}
            \end{vmatrix} &
            +
            \begin{vmatrix}
                a_{12} & a_{13} \\
                a_{22} & a_{23} \\
            \end{vmatrix} \\[1.5em]
            -
            \begin{vmatrix}
                a_{21} & a_{23} \\
                a_{31} & a_{33}
            \end{vmatrix} &
            +
            \begin{vmatrix}
                a_{11} & a_{13} \\
                a_{31} & a_{33}
            \end{vmatrix}&
            -
            \begin{vmatrix}
                a_{11} &  a_{13} \\
                a_{21} &  a_{23}
            \end{vmatrix} \\[1.5em]
            +
            \begin{vmatrix}
                a_{21} & a_{22} \\
                a_{31} & a_{32}
            \end{vmatrix} &
            -
            \begin{vmatrix}
            a_{11} & a_{12} \\
            a_{21} & a_{22}
            \end{vmatrix} &
            +
            \begin{vmatrix}
                a_{11} & a_{12} \\
                a_{21} & a_{22}
            \end{vmatrix}
        \end{pmatrix}
    \end{equation}
\end{document}