Sounds like he has started this early. Imagine there are people who want their children to walk early - no way! He is learning to express his independence and has realized that he can do what he wants. I wish I had a magic answer but you will just have to continue to say no - even though he probably won't get it until his 3+. Their urge to discover and make sense of their world is so strong and they really cannot remember you just said no. At this age, many babies are trying to make sure that things are consistent - they throw something on the floor and watch it fall. It is really them understanding how the physical world works. They will do it over an over and over. It's an addes bonus that it gets a rise out of mom!
I am sure you feel like you can only put so many things away and out of reach. But until they are able to reason, children are driven by their urges and the ones with the strong personalities will keep after something even after you have repeatedly said no. Great, they will have follow-through when they are older - the challenge is directing this while their little minds are really incapable of reasoning. The more you can do to make this less frustrating for yourself, the better you will confront it.
He probably sees you or you husband at the computer. Get him an old keyboard and everytime he goes for yours, tell him no and give him "his".