I think yes by definition (I can write with either hand), but I prefer the right hand for writing. Oddly, there are other things which I prefer my left hand to do; starting screws and nuts/bolts in places I can't see them, and for many fine-motor skill activities. My right hand is stronger physically, so I will use it to force a stuck jar lid, etc. What's very odd is that I'm a left-eye shooter but right eye dominant. I'm told that very few people are this way. I can't hit a beer can at 10 feet with my right eye, but I can hit a dime at 100 feet with my left eye. And it's nothing wrong with my right eye; I have "far better than perfect" vision in both eyes per my eye doctor.
Charles