The determinant of the matrix $F$ is calculated as $-1$, both using direct computation and by cofactor expansion. Since both methods give the same result, the calculation is consistent.

Do you need further details on the process, or have any questions? Here are some related questions for deeper understanding:

1. What is the cofactor expansion method for calculating a determinant?
2. How does the cofactor method differ from other determinant calculation techniques?
3. Can we apply the cofactor expansion to larger matrices? If so, how does it scale?
4. How is the determinant used in solving systems of linear equations?
5. What does a determinant of $-1$ signify for this matrix?

Tip: When expanding a determinant using cofactors, ensure you correctly alternate the signs starting from the top-left of the matrix.