The determinant of the given matrix is $171$.

Do you need any further details or clarifications?

Here are some related questions you might want to explore:

1. What does the determinant of a matrix represent geometrically?
2. How can you solve a system of equations using determinants (Cramer's Rule)?
3. What are the properties of determinants for square matrices?
4. How does row or column manipulation affect the determinant value?
5. How would the determinant change if a row or column had a constant factor?

Tip: The determinant is a scalar value that can give insights into properties of the matrix, such as invertibility. A non-zero determinant means the matrix is invertible.