整理下: 
使用: turnstile宏包
\xlongequal[r_{4}-r_{3}]{\substack{r_{3}-r_{2} \\ r_{3}-r_{2}}}使用:extarrows宏包
\ndtstile{{r_{4}-r_{3}}}{\substack{r_{3}-r_{2} \\ r_{3}-r_{2}}}
    \documentclass[10pt,a4paper]{article}
    \usepackage[utf8]{inputenc}
    \usepackage[T1]{fontenc}
    \usepackage{amsmath}
    \usepackage{amsfonts}
    \usepackage{amssymb}
    \usepackage{graphicx}
    \usepackage{extarrows}
    \usepackage{turnstile}
    \usepackage[left=2.00cm, right=2.00cm, top=2.00cm, bottom=2.00cm]{geometry}
    \begin{document}
    
    \[
    \left|\begin{array}{cccc}
    1 & 2 & 3 & 4 \\
    1 & 3 & 4 & 1 \\
    1 & 4 & 1 & 2 \\
    1 & 1 & 2 & 3
    \end{array}\right|
    \begin{aligned}
    & \xlongequal{\begin{array}{c}
    r_{3}-r_{2} \\[-2pt]
    r_{3}-r_{2} 
    \end{array}}\\[-7pt]
    &\begin{array}{c}
    ~ ~r_{4}-r_{3}
    \end{array} 
    \end{aligned}
    \left|\begin{array}{cccc}
    1 & 2 & 3 & 4 \\
    0 & 1 & 1 & -3 \\
    0 & 1 & -3 & 1 \\
    0 & -3 & 1 & 1
    \end{array}\right|
    \]
    
    \[
    \left|\begin{array}{cccc}
    1 & 2 & 3 & 4 \\
    1 & 3 & 4 & 1 \\
    1 & 4 & 1 & 2 \\
    1 & 1 & 2 & 3
    \end{array}\right|
    \xlongequal[r_{4}-r_{3}]{\substack{r_{3}-r_{2} \\ r_{3}-r_{2}}}
    \left|\begin{array}{cccc}
    1 & 2 & 3 & 4 \\
    0 & 1 & 1 & -3 \\
    0 & 1 & -3 & 1 \\
    0 & -3 & 1 & 1
    \end{array}\right|
    \]
    
    \[
    \left|\begin{array}{cccc}
    1 & 2 & 3 & 4 \\
    1 & 3 & 4 & 1 \\
    1 & 4 & 1 & 2 \\
    1 & 1 & 2 & 3
    \end{array}\right|
    \ndtstile{\displaystyle r_{4}-r_{3}}{\begin{array}{c}
    r_{3}-r_{2} \\[-2pt]
    r_{3}-r_{2} 
    \end{array}}
    \left|\begin{array}{cccc}
    1 & 2 & 3 & 4 \\
    0 & 1 & 1 & -3 \\
    0 & 1 & -3 & 1 \\
    0 & -3 & 1 & 1
    \end{array}\right|
    \]
    
    
    \[
    \left|\begin{array}{cccc}
    1 & 2 & 3 & 4 \\
    1 & 3 & 4 & 1 \\
    1 & 4 & 1 & 2 \\
    1 & 1 & 2 & 3
    \end{array}\right|
    \ndtstile{{r_{4}-r_{3}}}{\substack{r_{3}-r_{2} \\ r_{3}-r_{2}}}
    \left|\begin{array}{cccc}
    1 & 2 & 3 & 4 \\
    0 & 1 & 1 & -3 \\
    0 & 1 & -3 & 1 \\
    0 & -3 & 1 & 1
    \end{array}\right|
    \]
    
    \end{document}