The determinant of matrix $A$ is:

$\text{det}(A) = 842$

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you calculate the determinant of a 3x3 matrix?
2. What does the determinant tell us about the matrix?
3. Can a matrix with a zero determinant be inverted?
4. How do determinants relate to the area or volume in geometry?
5. What properties of a matrix affect its determinant?

Tip: If you swap two rows or columns in a matrix, the sign of the determinant will change, but its magnitude remains the same.