\documentclass[12pt]{article}
\usepackage{calc}
\usepackage{multido}
\usepackage{pstricks}
\pagestyle{empty}
\parindent=0pt
\makeatletter
\newdimen\xMax
\newdimen\yMax
\newcount\xLines
\newcount\yLines
\newdimen\dx
\newdimen\dy
\newcommand{\grid}[3][black]{{%
	\psset{linewidth=0.1pt}
	\xMax=#3%
    \yMax=#2%
    \dx=5mm  \xLines=\xMax \divide\xLines by \dx%
    \dy=5mm  \yLines=\yMax \divide\yLines by \dy%
    \advance\xLines by 1%
%    \advance\yLines by 1%
    \yMax=\dy \multiply\yMax by \yLines%
    \xMax=\dx \multiply\xMax by \xLines%
    \advance\xLines by 1%
    \advance\yLines by 1%
    \psgrid[subgriddiv=0,xunit=\dx,yunit=\dy,gridlabels=0pt,%
	gridcolor=black!20](\xMax,\yMax)
}}
\makeatother
\newsavebox{\gridbox}
\newenvironment{dogrid}[1][\linewidth]{%
  \begin{lrbox}{\gridbox}%
      \begin{minipage}{#1}%
}{%
      \end{minipage}%
  \end{lrbox}%
  \yMax=\dp\gridbox \advance\yMax by \ht\gridbox
  \noindent%
  \raisebox{-1.05\dp\gridbox}{\grid[lightgray]{\yMax}{\wd\gridbox}}%
  \usebox{\gridbox}
  \vspace{0.5cm}
}

\begin{document}

\begin{dogrid}
\[
\begin{array}{rcll}
y & = & x^{2}+bx+c\\
  & = & x^{2}+2\cdot{\displaystyle\frac{b}{2}x+c}\\
  & = & \underbrace{x^{2}+2\cdot\frac{b}{2}x+\left(\frac{b}{2}\right)^{2}}-{\displaystyle \left(\frac{b}{2}\right)^{2}+c}\\
 &  & \qquad\left(x+{\displaystyle \frac{b}{2}}\right)^{2}\\
 & = & \left(x+{\displaystyle \frac{b}{2}}\right)^{2}-\left({\displaystyle \frac{b}{2}}\right)^{2}+c & \left|+\left({\displaystyle \frac{b}{2}}\right)^{2}-c\right.\\
y+\left({\displaystyle \frac{b}{2}}\right)^{2}-c & = & \left(x+{\displaystyle \frac{b}{2}}\right)^{2} & \left|(\textrm{Scheitelpunktform})\right.\\
y-y_{S} & = & (x-x_{S})^{2}\\
S(x_{S};y_{S}) & \,\textrm{bzw.}\, & S\left(-{\displaystyle \frac{b}{2};\,\left({\displaystyle \frac{b}{2}}\right)^{2}-c}\right)
\end{array}
\]
\end{dogrid}

\begin{center}
\begin{dogrid}[.5\linewidth]
\[
\left(
\begin{array}{c@{}c@{}c}
\begin{array}{|cc|}
\hline
a_{11} & a_{12} \\
a_{21} & a_{22} \\
\hline
\end{array} & 0 & 0 \\
0 & \begin{array}{|ccc|}
    \hline
    b_{11} & b_{12} & b_{13}\\
    b_{21} & b_{22} & b_{23}\\
    b_{31} & b_{32} & b_{33}\\
    \hline
    \end{array} & 0 \\
0 & 0 & \begin{array}{|cc|}
        \hline
        c_{11} & c_{12} \\
        c_{21} & c_{22} \\
        \hline
        \end{array} \\
\end{array}
\right)
\]
\end{dogrid}
\end{center}

\end{document}
