It seems like I can’t do more advanced data analysis right now. Please try again later.

In the meantime, if you'd like, I can guide you through how to determine the inverse of the given matrix manually. Would you like that?

Here are some relative questions for deeper understanding:

1. What are the steps to calculate the inverse of a 3x3 matrix?
2. How can we check if a matrix has an inverse?
3. What is the significance of the determinant in matrix inversion?
4. How does the adjugate matrix relate to finding the inverse?
5. How do matrix inversions apply to solving systems of linear equations?

Tip: Always check if the determinant is zero before attempting to find the inverse of a matrix. If it is zero, the matrix does not have an inverse.