The Psalmist David was inspired when writing the Psalms...How do we know?
For David himself said by the Holy Ghost,
The LORD said to my Lord,
Sit thou on my right hand,
till I make thine enemies thy footstool.
Mark 12:46
The LORD said unto my Lord,
Sit thou at my right hand,
until I make thine enemies thy footstool.
Psalm 110:1