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I want to put the text A into the right bottom corner of the node rectangle without changing any other stuff. Please help me.

\documentclass[10pt]{standalone}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}
\draw [help lines] (0,0) grid (40pt,40pt);
\node [draw,minimum height = 30pt, minimum width = 30pt, inner sep = 0] at (15pt,15pt) {$A$};
\end{tikzpicture}
\end{document}

enter image description here

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up vote 6 down vote accepted

You can use a label to place some text inside the node:

\documentclass[10pt]{standalone}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}
\draw [help lines] (0,0) grid (40pt,40pt);
\node [draw,minimum height = 30pt, minimum width = 30pt, inner sep = 0, 
      label={[anchor=south east, draw=red, inner sep=0pt]south east:$A$}] 
      at (15pt,15pt) {$A$};
\end{tikzpicture}
\end{document}

enter image description here

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