Answer
See solution
Work Step by Step
The matrix representation in homogeneous coordinates of the linear transformation is $\left[\begin{array}{ll}A & 0 \\ 0^{T} & 1\end{array}\right]$
Matrix representation in homogeneous coordinates of the translation by the vector $p$ is $\left[\begin{array}{cc}I & p \\ 0^{T} & 1\end{array}\right]$
We get these transformations:
$\left[\begin{array}{cc}I & p \\ 0^{T} & 1\end{array}\right] \cdot\left[\begin{array}{cc}A & 0 \\ 0^{T} & 1\end{array}\right]=\left[\begin{array}{cc}A & p \\ 0^{T} & 1\end{array}\right]$
which is desired matrix.
