We discuss H and K observations of three fields in the bulge and disk of M31 obtained with the ALTAIR adaptive optics system and NIRI instrument on Gemini North. These are the highest resolution and deepest near-infrared observations obtained to date of the inner regions of M31 and demonstrate the promise of ground-based adaptive optics for studying the crowded regions of nearby galaxies. We have combined our observations with previously published Hubble Space Telescope Near-Infrared Camera and Multi-Object Spectrometer observations of nine M31 fields and have derived the coarse star formation histories of M31's bulge and inner disk. From fits to the MK luminosity functions, we find the stellar population mix to be dominated by old, nearly solar-metallicity stars. The old populations, which we define as having age >=6Gyr, indeed dominate the star formation histories at all radii independent of the relative contributions of bulge and disk stars. Although all of our fields contain some bulge contribution, our results suggest that there is no age difference between the bulge and disk to the limit of our precision.