Unit testing for object immutability

I want to make sure that a given group of objects is immutable.

I was thinking about something along the lines of:

1. check if every field is private final
2. check if class is final
3. check for mutable members

So I guess my question is: is 3. possible ?

I can check recursively whether every member of a class has its fields private final, but this is not enough since a class can have e method named getHaha(param) which adds the given param to an array for instance.

So is there a good way to check if an object is immutable or is it even possible ?

Thanks,