\documentclass[12pt]{article}
\usepackage{amsthm,amssymb,amsmath}
\usepackage[all]{xy}
\usepackage{pgf,pgfplots,tikz}
%\pgfplotsset{width=7cm,compat=newest}
\usepackage{xepersian}
\settextfont[Scale=1]{XB Niloofar}

\usetikzlibrary{snakes,arrows,matrix,shapes,backgrounds}

\begin{document}


$$
\begin{tikzpicture}[thick,>=stealth,->,shorten >=2pt,looseness=.5,auto,descr/.style={fill=white}]
\matrix [matrix of math nodes,row sep=10mm,column sep=10mm]
{
|(11)|A'&&  |(13)|S^{-1}A&&\\
&|(22)|S^{-1}_\beta A&&&  |(25)|(\alpha\leq \beta)\\
&&&&\\
&|(32)|S^{-1}_\alpha A&&& \\
};
\begin{scope}[every
node/.style={midway,auto,font=\scriptsize}]
\draw (11) -- node[] {$\varphi$} (13);
\draw (22) -- node[right] {$\rho_\beta$} (11);
\draw (22) -- node[left] {$\varphi_\beta$} (13);
\draw (32) -- node[left] {$\rho_\alpha$} (11);
\draw (32) -- node[right] {$\varphi_\alpha$} (13);
\draw [sloped,dotted](32) -- node[descr,near end] {$\rho_{\beta\alpha}$} (22);
\end{scope}
\end{tikzpicture}
$$
\end{document}