The determinant of the matrix $A$ using row reduction is approximately $\text{det}(A) = -352$.

Would you like more details on the steps of the row reduction method or have any further questions?

Here are some related questions:

1. What are the rules for performing row operations when finding a determinant?
2. How can row reduction simplify solving systems of linear equations?
3. What does the sign of the determinant tell us about a matrix?
4. How do we compute determinants for larger matrices (e.g., 5x5)?
5. Can a matrix with a zero determinant be invertible?

Tip: Always check if your matrix is singular (determinant is zero) before trying to invert it!