an edge connecting multiple nodes

Question

I want to draw an edge that connects multiple nodes. I am able to achieve this using the ''to'' feature as shown in example below:

\documentclass[convert={density=300,size=1080x800,outext=.png}]{ standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
 \matrix (m)[column sep=.5in, row sep=.5in,  ampersand replacement=\&]{
      \node[] (r1c1) {}; \& \node[] (r1c2) {}; \& \node[] (r1c3) {};  \\
      \node[] (r2c1) {}; \& \node[] (r2c2) {}; \& \node[] (r2c3) {};  \\
      };
      \draw (r1c1)  to[<-]  (r2c1.center) to (r2c2.center) to (r1c2);
\end{tikzpicture}
\end{document}

The output looks as follows:

I am not able to change the property of the individual segment or connectors. For e.g. tikz discarded the directive for putting an arrow on the first leg of the connected. What I want to achieve to begin with is rounded corners.

Just to follow up along this line, below are three ways to achieve edge through multiple nodes

\documentclass[convert={density=300,size=1080x800,outext=.png{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
 \matrix (m)[column sep=.5in, row sep=.5in,  ampersand replacement=\&]{
      \node[] (r1c1) {}; \& \node[] (r1c2) {}; \& \node[] (r1c3) {};  \\
      \node[] (r2c1) {}; \& \node[] (r2c2) {}; \& \node[] (r2c3) {};  \\
      };
      \draw (r1c1)  edge  (r2c1.center) edge (r2c2.center) edge (r1c2);
\end{tikzpicture}

\begin{tikzpicture}
 \matrix (m)[column sep=.5in, row sep=.5in,  ampersand replacement=\&]{
      \node[] (r1c1) {}; \& \node[] (r1c2) {}; \& \node[] (r1c3) {};  \\
      \node[] (r2c1) {}; \& \node[] (r2c2) {}; \& \node[] (r2c3) {};  \\
      };
      \draw (r1c1)  --  (r2c1.center) --  (r2c2.center) -- (r1c2);
\end{tikzpicture}
\end{document}

The output of which looks as follows:

Using edge doesn't work, but would have been the most flexible one.

Answer 1

Like this?

\documentclass[tikz, border=3mm]{standalone}

\begin{document}
\begin{tikzpicture}
\matrix (m) [column sep=.5in, row sep=.5in,  ampersand replacement=\&]{
      \node[] (r1c1) {}; \& \node[] (r1c2) {}; \& \node[] (r1c3) {};  \\
      \node[] (r2c1) {}; \& \node[] (r2c2) {}; \& \node[] (r2c3) {};  \\
      };
\draw[rounded corners,<-] (r1c1)  |- (r2c2.center) -- (r1c2);
\end{tikzpicture}
\end{document}

Addendum: Functions of nodes in matrix is not very clear. Concerning only the curve, the same result you can obtain with:

\documentclass[tikz, border=3mm]{standalone}
\usetikzlibrary{matrix}

\begin{document}
\begin{tikzpicture}
\matrix (m) [matrix of nodes, nodes in empty cells,
             column sep=.5in, row sep=.5in]
{
   &   &    \\
   &   &    \\
};
\draw[rounded corners,<-] (m-1-1)  |- (m-2-2.center) -- (m-1-2);
\end{tikzpicture}
\end{document}