If you don't check ID then anyone with a list of registered-but-unlikely voters (or who registers unlikely voters ahead of time without their knowledge) could be voting multiple times and there is nothing to detect it. If you check ID then that doesn't happen as easily, but you still have no way to know if it would have happened in the alternative.
The closest thing to knowing would be if apparent turnout declines in response to checking ID, but a) different elections have different turnout anyway and b) even if you could detect a significant change, one party would then argue that it's a reduction in fraud and the other would argue that checking ID is reducing legitimate turnout, and you still don't know which one it is -- it could even be both.
In fact this is done regularly.
We know for a statistical fact that there is no meaningful amount of this type of fraud (unless you're also supposing that these people somehow also acquire a copy of each person's signature).
Why do you believe what you believe? What would be true if it were false? Is that a thinkable alternative? If not, do you really have a hypothesis, or do you have a political belief being presented in the guise of a claim of fact?
If what you believe to be true is in fact true, then you should be able to comfortably go searching for evidence to falsify it and support the alternative, and fail to find such evidence, confident in your assumption that you won't find it. Either way, I hope that you desire to find the correct answer rather than the one that would be convenient for your political position, and that whatever hypothesis you have has not set itself up to be unfalsifiable.