Enlarge the flag by a scale factor of $2$ about the first centre of enlargement. Now enlarge the resulting flag by a scale factor of $\frac{1}{2}$ about the second centre of enlargement. Can you find a single transformation that takes the first flag to the last flag?
Now try changing the scale factors so that the first enlargement is by scale factor $3$ and the second by scale factor $\frac{1}{3}$. Try some other similar pairs (remembering that if the first scale factor is $k$ then the second one should be $\frac{1}{k}$).
Describe what will happen if the first scale factor is $k$ and the second $\frac{1}{k}$?