Answer
See below
Work Step by Step
We know $A$ is an $m \times n$
$A=\begin{bmatrix}
a_{11} & a_{12} & ...& a_{1n}\\
a_{21} & a_{22} & ...& a_{2n}\\
. & . & ... & .\\
a_{m1} & a_{m2} & ...& a_{mn}\\
\end{bmatrix}$
and $D=diag(d_1,d_2,...,d_n)\\
D=\begin{bmatrix}
d_{11} & 0 & ...&0\\
0 & d_{22} & ...& 0\\
. & . & ... & .\\
0 & 0 & ...& d_{nn}\\
\end{bmatrix}$
We obtain: $AD=\begin{bmatrix}
a_{11} & a_{12} & ...& a_{1n}\\
a_{21} & a_{22} & ...& a_{2n}\\
. & . & ... & .\\
a_{m1} & a_{m2} & ...& a_{mn}\\
\end{bmatrix}\begin{bmatrix}
d_{11} & 0 & ...&0\\
0 & d_{22} & ...& 0\\
. & . & ... & .\\
0 & 0 & ...& d_{nn}\\
\end{bmatrix}\\=\begin{bmatrix}
a_{11}d_{11} & a_{12}d_{12} & ...& a_{1n}d_{nn}\\
a_{21} d_{21} & a_{22}d_{22} & ...& a_{2n}d_{nn}\\
. & . & ... & .\\
a_{m1}d_{11} & a_{m2}d_{22} & ...& a_{mn}d_{nn}\\
\end{bmatrix}\\
\begin{bmatrix}
=a_{ij} d_{jj}
\end{bmatrix}\\
=\begin{bmatrix}
a_{j}dj
\end{bmatrix}$
where $1\leq j\leq m$ and $1\leq j\leq n$
We can see that $AD$ is the matrix obtained
by multiplying the j-th column vector of A by $d_{jj}$ , where $1 ≤ j ≤ n$
