I try to reproduce the figure but I am unable to adjust the arrows between the nodes of the matrices
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{matrix,decorations.pathreplacing, calc, positioning,fit}
\tikzset{arrow style mul/.style={circle,midway,fill=white}}
\begin{document}
\begin{tikzpicture}
[thick,baseline=(A.center),>=stealth,
every left delimiter/.append style={name=rd},thick]
\matrix [matrix of math nodes,left delimiter=(,right delimiter=)]
(A) at (0,0) {
|[red]| a & |[blue]|b \\
c & d \\
};
\matrix [matrix of math nodes,left delimiter=(,right delimiter=)]
(P) at (4cm,0) {
|[green]| ae + bf \\
ce + df \\
};
\matrix [matrix of math nodes,left delimiter=(,right delimiter=)]
(B) at (4cm,2cm) {
|[red]| e \\
|[blue]| f \\
};
\draw[red,->](A.north -|A-1-1) --
node[arrow style mul] (x) {$\times$} (rd.west|-B-1-1.center);
\draw[blue,->](A.north -|A-1-2) --
node[arrow style mul] (x) {$\times$} (rd.west|-B-2-1.center);
\end{tikzpicture}
\end{document}