Draw augmented matrix in tikz

Question

I'm trying to create a very simple matrix in Tikz: can anybody help me with this? The matrix should look like this:

Thank you in advance for all your help!

Answer 1

Should it be (s+t)^2=2s^2? In this case:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[scale=3]
\draw (0,0) -- (1.412,0) -- (1.412,-1.412) -- (0,-1.412) -- cycle;
\draw (0,0) -- (1,0) -- (1,-1) -- (0,-1) -- cycle;
\node at (.5,.2) {\Large $s$};
\node at (1.206,.2) {\Large $t$};
\node at (-.2,-.5) {\Large $s$};
\node at (-.2,-1.206) {\Large $t$};
\end{tikzpicture}

\end{document}

Edit: Thanks to @TomBombadil for pointing out that the above tikzpicture can be improved this way:

\begin{tikzpicture}[scale=3]
\draw (0,0) rectangle ({sqrt(2)},{-sqrt(2)});
\draw (0,0) rectangle (1,-1);
\node at (.5,.2) {\Large $s$};
\node at (1.206,.2) {\Large $t$};
\node at (-.2,-.5) {\Large $s$};
\node at (-.2,-1.206) {\Large $t$};
\end{tikzpicture}