Does DNA change? If it doesn't, and we are all descendants of Adam and Eve, why isn't our DNA the same?

I'm not trying to bash anyone. I DO believe in God and in Adam and Eve. But I was reading this thing about a frozen corpse or something like that from hundreds or thousands of years ago who was tested and turned out to be an ancestor of some teacher. Anyway, that got me thinking, if DNA always remains the... show more I'm not trying to bash anyone. I DO believe in God and in Adam and Eve. But I was reading this thing about a frozen corpse or something like that from hundreds or thousands of years ago who was tested and turned out to be an ancestor of some teacher.

Anyway, that got me thinking, if DNA always remains the same and Adam and Eve were the first man and woman and we are all descendants, shouldn't we have the same DNA? (I don't mean exact, I mean in the way that we can tell 2 people are related or not.)

It's just an innocent question, I'm not trying to prove or disprove anything. What I'm saying could be the stupidest thing you've ever heard, but seriously, this question keeps bugging me.
Update: Keep those answers coming! By the way, like I said, I don't mean exact DNA, I know that each person has a unique set of their own DNA, I mean the same thing that scientists test to see if 2 people are related or not. They test DNA. I don't mean, "why aren't we clones?" I mean why isn't... show more Keep those answers coming!

By the way, like I said, I don't mean exact DNA, I know that each person has a unique set of their own DNA, I mean the same thing that scientists test to see if 2 people are related or not. They test DNA. I don't mean, "why aren't we clones?" I mean why isn't there some faint trace of blood connection between us if we came from the same set of parents (Adam and Eve)?
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