Aligning diagram with arrows

Welcome to TeX-SE! I recommend tikz-cd for that.

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}[column sep=3em,row sep=3em]
M_n(D) \arrow[r,"\alpha'"] \arrow[d,"\det"]  & M_n(R)\arrow[d,"\det"]\\
D \arrow[r,"\alpha"] &R 
\end{tikzcd}
\end{document}

If needed, you can make det larger. (The font sizes of the \alphas can be increased in the same way.)

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}[column sep=3em,row sep=3em]
M_n(D) \arrow[r,"\alpha'"] \arrow[d,"\displaystyle\det"]  & M_n(R)\arrow[d,"\displaystyle\det"]\\
D \arrow[r,"\alpha"] &R 
\end{tikzcd}
\end{document}

Considering that I absolutely agree with the very good user @marmot, I add another code using xy package. Look closely at the almost similar comparison between tikz-cd and xy, except for the tips of the arrows.

\documentclass{book}
\usepackage[all]{xy}
\begin{document}
\xymatrix@R=3pc@C=3pc{
M_n(D) \ar[r]^{\alpha'} \ar[d]^{\det} & M_n(R) \ar[d]^{\det}\\
D \ar[r]^{\alpha} & R\\
}
\end{document}

If you add only cmtip, you can obtain the same tips of tikz-cd.

\documentclass{book}
\usepackage[all,cmtip]{xy}%%%%%%%% <---------add only cmtip
\begin{document}
\xymatrix@R=3pc@C=3pc{
M_n(D) \ar[r]^{\alpha'} \ar[d]^{\det} & M_n(R) \ar[d]^{\det}\\
D\ar[r]^{\alpha} & R\\
}
\end{document}