A matrix representation of certain matrix in LaTeX

Question

How can we write the following statement with the matrix form in the LaTeX ? (We wish to represent it in the matrix form)

By $\delta_{ij}(a)$  we mean a n by n matrices 
in $M_n(\mathbb{R})$ which has only one nonzero 
entry $a$ at $i$, th row and j th column.

Answer 1

If I understand well, is it something like this you want?

\documentclass{article}
\usepackage{fourier}
\usepackage{amsmath}
\usepackage{blkarray, bigstrut}

\begin{document}

\begin{equation*}
  \begin{blockarray}{rl@{}c@{}r}
    & & \makebox[0pt]{column $j$} \\[-0.5ex]
    & & \,\downarrow \\[-0.5ex]
    \begin{block}{r(l@{}c@{}r)}
    & \makebox[3.1em]{\Large $0$\bigstrut[t]} & \vdots &\makebox[4.2em]{\Large $0$} \\[-0.2ex]
    \text{row }i \to \mkern-9mu & \raisebox{0.5ex}{\makebox[3.2em][l]{\dotfill}} & 1 & \raisebox{0.5ex}{\makebox[4.2em][r]{\dotfill}} \\[-1ex]
    & \makebox[3.1em]{\Large $0$} & \vdots &\makebox[4.2em]{\bigstrut\Large $0$} \\
    \end{block}
  \end{blockarray}
\end{equation*}

\end{document} 

Answer 2

With {NiceMatrix} of the package nicematrix.

\documentclass{article}
\usepackage{nicematrix}
\usepackage{tikz}

\begin{document}

\NewDocumentCommand{\zero}{}{\Block{}<\Large>{0}}

$\begin{NiceMatrix}[nullify-dots,columns-width=4mm,xdots/shorten=5pt]
\CodeBefore
  \SubMatrix({3-2}{5-4})
\Body
                  &        & \clap{column $j$}   \\
                  &        & \downarrow          \\[1mm]
                  & \zero  & \Vdots     & \zero  \\
\text{row } i \to & \Cdots & 1          & \Cdots \\
                  & \zero  & \Vdots     & \zero 
\end{NiceMatrix}$

\end{document}

You need several compilations (because nicematrix uses PGF/Tikz nodes under the hood).