How to add vertical rule between two horizontally aligned minipages?

Question

I need to have a vertical rule between the text and an image. paracol package breaks across pages. I do not want to have that.

\documentclass[a5paper]{scrbook}

\usepackage{adjustbox}
\usepackage{tikz}


\begin{document}

\begin{adjustbox}{valign=t,minipage={.45\textwidth}}
\[
a=b
\]
\end{adjustbox}
\begin{adjustbox}{valign=t,minipage={.45\textwidth}}
\begin{tikzpicture}
\draw [thick,red] (0,0) rectangle (2,1);
\end{tikzpicture}
\end{adjustbox}

\end{document}

With multicol the text and image alignment is wrong.

\documentclass[a5paper]{scrbook}
%
\usepackage{tikz}
\usepackage{multicol}
\setlength\columnseprule{.4pt}
\begin{document}
\begin{multicols}{2}
\[
a=b
\]
\columnbreak
\begin{tikzpicture}
\draw [thick,red] (0,0) rectangle (2,1);
\end{tikzpicture}
\end{multicols}
\end{document}

Answer 1

\documentclass[a5paper]{scrbook}
%
\usepackage{tikz}
\usepackage{multicol}
\setlength\columnseprule{.4pt}
\begin{document}
\begin{multicols}{2}
First line
\vfill
\[
a=b
\]
\vfill
Last 
\columnbreak

\begin{tikzpicture}
\draw [thick,red] (0,0) rectangle (2,5);
\end{tikzpicture}
\end{multicols}

\end{document}