Prove there is a matrix B

Let be an matrix and suppose that is an matrix such that every column of is in the column space of . Prove there is a matrix such that

[Hint: we know that the equation has a solution if and only if ]

I don't know if this is exactly how the question is meant to be said. Our Prof. made a severe typo in the original, so I'm asking him to simply rewrite the question in its intended form rather than just provide us with a quick correction (which could be easily misinterpreted).