The determinant of the matrix $A$ is $\det(A) = 3516$.

Would you like further details or clarification on this? Here are 5 related questions to explore:

1. How can determinants be used to solve systems of linear equations?
2. What is the geometric interpretation of a determinant for a 2x2 or 3x3 matrix?
3. How does the determinant change when performing row operations on a matrix?
4. How is the cofactor expansion method applied to find a matrix determinant?
5. What properties of a matrix can we infer from its determinant?

Tip: A matrix with a determinant of zero is singular, meaning it doesn't have an inverse.