Add text to matrix row or column

Question

Can a single column and row be highlighted within a matrix ? Would like to add some text and arrow that describes a given row within a matrix, something like :

latex code for above matrices :

\begin{gather*}
\begin{bmatrix}
  1 & 2 & 3 \\ 1 & 2 & 3
\end{bmatrix}
*
\begin{bmatrix}
  1 & 2 & 3 \\ 1 & 2 & 3
\end{bmatrix}
\end{gather*}

Answer 1

It's very easy with tikz:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{positioning, arrows.meta}
\tikzset{%
    myarrow/.style = {-Stealth, shorten >=5pt}
} 
\newcommand{\mypoint}[2]{\tikz[remember picture]{\node[inner sep=0, anchor=base](#1){$#2$};}}

\begin{document}
    blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah
    \begin{gather*}
    \begin{bmatrix}
    1 & 2 & 3 \\ \mypoint{here1}{1} & 2 & 3
    \end{bmatrix}
    *
    \begin{bmatrix}
    1 & 2 & \mypoint{here2}{3} \\ 1 & 2 & 3
    \end{bmatrix}
    \end{gather*}
    \begin{tikzpicture}[remember picture, overlay]
      \node[below=30pt of here1](textofhere1){some text};
      \draw[myarrow] (textofhere1) -- (here1);
      \node[right=30pt of here2](textofhere2){some other text};
      \draw[myarrow] (textofhere2) -- (here2);
    \end{tikzpicture}
    \vspace{7ex}

    blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah
\end{document}

Answer 2

With pstricks:

\documentclass[11pt, svgnames]{article}
\usepackage{amsmath}
\usepackage{pst-node}
\usepackage{auto-pst-pdf} %% to compile with pdflatex --enable-write18 (MiKTeX) or pdflatex -shell-escape (TeXLive, MacTeX)

\begin{document}

\[ \begin{pspicture}
    \begin{bmatrix}
      1 & 2 & 3 \\ \rnode{B}{1} & 2 & 3
    \end{bmatrix}
    *
    \begin{bmatrix}
      1 & 2 & \rnode{T}{3} \\ 1 & 2 & 3
    \end{bmatrix}
    \psset{labelsep = 2em, nodesepA = 0.3ex, nodesepB = 0.8ex, arrows = ->, arrowinset = 0.12, linewidth = 0.6pt, linecolor = Tomato}
    \everypsbox{\color{Tomato}}
    \uput[r](T){\rnode{T1}{\text{Text1}}}\ncline{T1}{T}
    \uput[d](B){\rnode{T2}{\text{Text2}}}\ncline{T2}{B}
  \end{pspicture} \]

\end{document} 

(If you don't want to compile with pdflatex, remove loading of auto-pst-pdf)

Answer 3

If it's OK to have the arrows above the matrix, you could (ab)use the gmatrix environment from the gauss package to place them. Two possibilities for making the arrows are shown.

No \vspace required.

\documentclass{article}
\usepackage{amsmath,gauss,tikz}
% modify some things in gmatrix environments
\renewcommand\rowmultlabel{}
\renewcommand\colmultlabel{}
\setlength\rowarrowsep{0pt}
\setlength\rowopminsize{0pt}
\begin{document}
Some text text text text and so on.
\begin{equation*}
\begin{gmatrix}[b]
  1 & 2 & 3 \\
  1 & 2 & 3
\colops
\mult{0}{\begin{array}{c}\text{text 1}\\\downarrow\end{array}}
\end{gmatrix}
\!*
\begin{gmatrix}[b]
  1 & 2 & 3 \\
  1 & 2 & 3
\rowops
\mult{0}{\leftarrow\text{text 2}}
\end{gmatrix}
\end{equation*}
More text text text text text and so on.
\begin{equation*}
\begin{gmatrix}[b]
  1 & 2 & 3 \\
  1 & 2 & 3
\colops
\mult{0}{\tikz\draw[<-](0,0)--(0,5mm)node[above]{text 1};}
\end{gmatrix}
\!*
\begin{gmatrix}[b]
  1 & 2 & 3 \\
  1 & 2 & 3
\rowops
\mult{0}{\tikz[baseline=(a.base)]\draw[<-](0,0)--(5mm,0)node[name=a,right]{text 2};}
\end{gmatrix}
\end{equation*}
\end{document}