The designer of class Matrix must have been a fan of immutable data structures and functional programming. Yes, you are correct.
In any case, there is a simple solution for what you want. Use Matrix for what it can do, then, just use .to_a to get a real array.
>> Matrix.identity(2).to_a
=> [[1, 0], [0, 1]]
See also Numerical Ruby Narray. You could also monkeypatch the class to add more behavior. If you do this, please patch a subclass of Matrix. (There are Ruby library projects out there that want more behavior from required classes so they directly modify them, making their new files somewhat toxic. They could have so easily just patched a subclass or singleton class.)
Oh, and khelll (:-) would probably like me to say that there is quite possibly a way for you to do what you want in a functional style. That is, by creating new objects rather than by modifying the old ones.