Unless you plan to do other recreational riding, touring, etc., I would simply walk to work for that distance. It would be just as much or more exercise, and much simpler and cheaper. A reasonably fit person should be able to walk 1.5 miles easily in 30 minutes. It probably would take almost that long to ride a bike when you factor in the time taken to get prepared and pack your gear in the morning, ride to work, and lock it up.

However, if you view commuting as an entry point -- or gateway drug -- to cycling, start commuting by all means. It's a great sport/hobby for overall fitness as well as fun.