Align many matrices and operations so it's more beautiful

I thought I'd use nicematrix package: https://ctan.org/pkg/nicematrix . You can see that the matrices are all the same. On each row you can make the transformations by row and by column as in the minimal example I showed you. I don't know if this can correspond to what you are looking for.

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\usepackage{nicematrix}

\usepackage[left=.1in, right=.5in]{geometry}

\begin{document}
\[
\begin{matrix}
\begin{bNiceArrayC}{CCCC}
1 & 1 & 1 & 6z-2 & \\
-1 & 2 & 0 & 4z-5 & R_2-(-1)R_1\rightarrow R_2 \\
1 & 0 & -1 & z-3 & \\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} & \hspace{4cm} \begin{bNiceArrayC}{CCCC}
1 & 1 & 1 & 6z-2 & \\
0 & 3 & 1 & 10z-7 & \\
1 & 0 & -1 & z-3 & R_3-1R_1\rightarrow R_3\\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} \\[2cm]
\begin{bNiceArrayC}{CCCC}
1 & 1 & 1 & 6z-2 & \\
-1 & 2 & 0 & 4z-5 & R_2-(-1)R_1\rightarrow R_2 \\
1 & 0 & -1 & z-3 & \\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} & \hspace{4cm} \begin{bNiceArrayC}{CCCC}
1 & 1 & 1 & 6z-2 & \\
0 & 3 & 1 & 10z-7 & \\
1 & 0 & -1 & z-3 & R_3-1R_1\rightarrow R_3\\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} \\[2cm]
\begin{bNiceArrayC}{CCCC}
1 & 1 & 1 & 6z-2 & \\
-1 & 2 & 0 & 4z-5 & R_2-(-1)R_1\rightarrow R_2 \\
1 & 0 & -1 & z-3 & \\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} & \hspace{4cm} \begin{bNiceArrayC}{CCCC}
1 & 1 & 1 & 6z-2 & \\
0 & 3 & 1 & 10z-7 & \\
1 & 0 & -1 & z-3 & R_3-1R_1\rightarrow R_3\\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} \\
\end{matrix}
\]
\end{document}

Or you can adapt this code using your matrix(s):

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\usepackage{nicematrix}

\usepackage[left=.1in, right=.5in]{geometry}

\begin{document}
\[
\begin{matrix}
\begin{bNiceArrayC}{CCC|C}
1 & 1 & 1 & 6z-2 & \\
-1 & 2 & 0 & 4z-5 & R_2-(-1)R_1\rightarrow R_2 \\
1 & 0 & -1 & z-3 & \\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} & \hspace{4cm} \begin{bNiceArrayC}{CCC|C}
1 & 1 & 1 & 6z-2 & \\
0 & 3 & 1 & 10z-7 & \\
1 & 0 & -1 & z-3 & R_3-1R_1\rightarrow R_3\\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} \\[2cm]
\begin{bNiceArrayC}{CCC|C}
1 & 1 & 1 & 6z-2 & \\
-1 & 2 & 0 & 4z-5 & R_2-(-1)R_1\rightarrow R_2 \\
1 & 0 & -1 & z-3 & \\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} & \hspace{4cm} \begin{bNiceArrayC}{CCC|C}
1 & 1 & 1 & 6z-2 & \\
0 & 3 & 1 & 10z-7 & \\
1 & 0 & -1 & z-3 & R_3-1R_1\rightarrow R_3\\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} \\[2cm]
\begin{bNiceArrayC}{CCC|C}
1 & 1 & 1 & 6z-2 & \\
-1 & 2 & 0 & 4z-5 & R_2-(-1)R_1\rightarrow R_2 \\
1 & 0 & -1 & z-3 & \\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} & \hspace{4cm} \begin{bNiceArrayC}{CCC|C}
1 & 1 & 1 & 6z-2 & \\
0 & 3 & 1 & 10z-7 & \\
1 & 0 & -1 & z-3 & R_3-1R_1\rightarrow R_3\\
1 & 2 & 0 & 8z-7 & \\
\end{bNiceArrayC} \\
\end{matrix}
\]
\end{document}