Finding a Matrix from Determinants I've stumbled upon this problem on my homework, and I have no clue how to do it, and haven't found any help online:

If I'm understanding this correctly, then $det(M) = ad - cb + eh - gf$ ?
What I don't get is how to find M from knowing this information.
Are there any suggestions on how to solve this?

It's unclear what the dimension of $M$ should be, but here is a start to a solution where $M$ is a $2\times 2$ matrix:
$$\begin{pmatrix}a&??\\1&d\end{pmatrix}$$
Try to finish it from here (i.e., find what goes in the entry labeled $??$).
