Answer
See explanation
Work Step by Step
Make the transformation matrices in homogeneous cordinates for the dilation, rotation, and translation be called respectively $D,$ and $R,$ and $T$.
\[
D=\left[\begin{array}{lll}
s & 0 & 0 \\
0 & s & 0 \\
0 & 0 & 1
\end{array}\right], R=\left[\begin{array}{ccc}
\cos \varphi & -\sin \varphi & 0 \\
\sin \varphi & \cos \varphi & 0 \\
0 & 0 & 1
\end{array}\right], T=\left[\begin{array}{ccc}
1 & 0 & h \\
0 & 1 & k \\
0 & 0 & 1
\end{array}\right]
\]
Get products of these matrices to see which transformations are commute.
\[
\begin{array}{l}
D R=\left[\begin{array}{ccc}
s \cos \varphi & -s \sin \varphi & 0 \\
s \sin \varphi & s \cos \varphi & 0 \\
0 & 0 & 1
\end{array}\right] \\
R D=\left[\begin{array}{ccc}
s \cos \varphi & -s \sin \varphi & 0 \\
s \sin \varphi & s \cos \varphi & 0 \\
0 & 0 & 1
\end{array}\right]
\end{array}
\]
$D$ and $R$ commute.
\[
D T=\left[\begin{array}{ccc}
s & 0 & s h \\
0 & s & s k \\
0 & 0 & 1
\end{array}\right]
\]
\[
T D=\left[\begin{array}{lll}
s & 0 & h \\
0 & s & k \\
0 & 0 & 1
\end{array}\right]
\]
$D \text { and } T \text { do no commute (they commute only when } s=1)$
\[
\begin{array}{l}
R T=\left[\begin{array}{ccc}
\cos \varphi & -\sin \varphi & h \cos \varphi-k \sin \varphi \\
\sin \varphi & \cos \varphi & h \sin \varphi+k \cos \varphi \\
0 & 0 & 1
\end{array}\right] \\
T R=\left[\begin{array}{ccc}
\cos \varphi & -\sin \varphi & h \\
\sin \varphi & \cos \varphi & k \\
0 & 0 & 1
\end{array}\right]
\end{array}
\]
$T \text { and } R \text { do not commute (they commute only when } \varphi=0)$
