Currency arbitrage across many currencies

You are given an $n \times n$ matrix rates where rates[i][j] is how many units of currency $j$ you get for one unit of currency $i$. Write a function that returns whether some cycle of conversions turns 1 unit of a currency into more than 1 unit of the same currency. State the complexity.

Test it on three currencies USD, EUR, JPY with USD→EUR 0.9, EUR→JPY 160 and JPY→USD 0.0070. Fill each reverse rate with the reciprocal (EUR→USD is $1/0.9$, and so on) and put 1 on the diagonal.