Look What You're Doing to Me is written in the key of A♭ Major.
According to the Theorytab database, it is the least popular key among Major keys and the 19th most popular among all keys. Major keys, along with minor keys, are a common choice for popular songs. The three most important chords, built off the 1st, 4th and 5th scale degrees are all major chords (A♭ Major, D♭ Major, and E♭ Major).
See the A♭ Major Cheat Sheet for popular chords, chord progressions, downloadable midi files and more!