Currently, the Moon is tidally locked to the Earth but the Earth is not tidally locked to the Moon.
In your scenario (which could be accomplished by raising the mass of the Earth), where the Moon has an orbital and rotational period of 24 hours, the two bodies are mutually tidally locked.
Indeed, the Earth-Moon system is gradually moving toward such a state due to tidal energy exchange -- albeit through slowing of the Earth's rotation rather than shortening of the Moon's orbit.