documentclass{article}
    usepackage{tikz}
    usetikzlibrary{matrix}
    usepackage{mathtools}
    usepackage{float}

    begin{document}
        [
        det(A) = begin{vmatrix*}[r]
        a & b & c\
        d & e & f\
        g & h & i
        end{vmatrix*}
        ]
        begin{figure}[H]
            centering
            $ det(A) =$
            begin{tikzpicture}[
            baseline=(A-2-1.base),
            every left delimiter/.style={xshift=.8em},
            every right delimiter/.style={xshift=-.8em},
            ]
            matrix [
            matrix of math nodes,
            row sep={0.43cm,between origins},
            column sep={0.6cm,between origins},
            left delimiter=|,
            right delimiter=|] (A)
            {
                a & b & c \
                d & e & f \
                g & h & i \
            };

            draw[line width=0.6pt] (A-1-1.center) -- (A-3-3.center);
            draw[line width=0.6pt] (A-2-1.center) -- (A-3-2.center) -- (A-1-3.center) -- (A-2-1.center)--cycle;
            end{tikzpicture}
        end{figure}

    end{document}