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I'm actually not quite sure how this happened but I learned to write right-handed but my natural inclination is to do just about everything else left-handed.
And it's worth noting I write "ok" left handed without much practice; that is to say, my handwriting is atrocious either way.
I have a friend who swears he's ambidextrous. The reason is that he writes and eats right-handed despite always being a lefty in sports.
I said "If I spit in your face right now which hand would you swing at me with?" He said "My left." I said "Well that means you're left-handed."
Being able to do some things with the opposite hand generally means you learned it that way for some reason or another. But you probably still have a naturally dominant side, writing with your right but playing tennis with your left doesn't mean you're "ambidextrous." I think there are truly ambidextrous people but they are quite rare.