This is a practice question to a test I will be taking soon. My conjecture is that it's none of the choices given. I tried reflections about y=x, y-axis, x-axis and it doesn't work. Does anyone agree?
The correct answer on the test should be $A$.
However, you could make a convincing argument for case $B$, because theoretically, you can do this with two reflections. You first reflect $ABC$ about $y=x$, so it is in the same location as $A'B'C'$. Then you set up a reflection along an axis that goes through the middle of the triangle (a straight line from negative $y$ to positive $x$) to reflect the triangle exactly such that all the points match.
I don't expect that sort of argument to be required.
If you use during the transformation odd number of reflection than final triangle would have opposite orientation ie. ABC would go in anti-clockwise order. This rules out II and III.
That the answer is I is already given by Newb.