When do I need to add a hash to my own object, for example a python data class?

Question

I find myself in one of two situations very often. I have a class, either a standard class

class myClass:
    def __init__(self, x):
        self.x = x

or a dataclasss

@dataclass(frozen=True)
class myClass:
    x: float

Now, all I want is to be able to store these two classes as keys in a dictionary, such that the hash is on the instant of the object itself, so look-up will work if (and only if) I look-up using the exact same instant of the object that I stored as key.

I've read online a bit, and what confuses me is the __eq__ operator. I have no idea why that is relevant here. All I want is for dictionaries to remember the object by its id. So, my questions are

1. do I need to add def __hash__(self): return id(self) to any of those two objects above, or is this always implicit?
2. do I need to add __eq__?