Economics - triangular arbitrage

Reference to Kaplan, book 1, pg 273. The question asks about a triangular arbitrage of three pairs (USD/AUD, USD/MXN, MXN/AUD). They worked out the question by constructing a triangle starting from the USD going to MXN, then AUD and finally back to the USD. On the other hand, the assumed going counterclockwise will be as follows, USD to AUD to MXN and then back to USD. My question is how did they decide which one is the first currency to convert into (AUD or MXN)??? because that decides whether you’re going clockwise or the other way round, and both give completely different answers!

I did some more reading, and I think we have to do it both ways to figure out whether an arbitrage opportunity does exist!

I always suggest doing it one way, then the other.

If you get a profit the first way, you don’t need to do the second: you have your answer.