Multiple variables correlation

Question

There are a number of entities. Each entity has three sets of parameters. Each set of parameters describes entity behaviour in a specific system. The problem is to find mathematical method that would answer the question what systems correlate between each other. Which means that their parameters corelate between each other.
Here is the example. There are three systems X, Y and Z. The dataset looks like this:
№  X1  X2  Y1  Y2  Z1  Z3
1  0.5  0.7  0.8  0.1  0.9  0.8
2  0.1  0.2  0.4  0.5  0.1  0.9
3  0.1  0.1  0.1  0.2  0.1  0.1
...
The task is to tell what systems correlate. For instance, do X and Y correlate?
Does anyone know a method to do this?