For writing, I am left handed, and its well annoying because when i right it is smudgy. So, i learnt to write properly with my right hand. Now my handwriting is much better and clearer!
I do most things right handed, because all the people in my family are right handed and I guess I just copied them in the way that they do things. You are ambidextrous, as was said earlier, but who cares about which hand you use? Typing - you use both hands - you dont get people saying "oo im right handed so i can type words faster than you," do you. (if so, take them to a doctor)
Hope it helps !