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The inverse of matrix \( C \) is:

\[
C^{-1} = \begin{pmatrix}
0 & 2 & -1 \\
-1 & -1 & 0 \\
-3 & -4 & 1
\end{pmatrix}
\]

Looking at the provided options, this corresponds to option **c**.

Would you like further clarification or a step-by-step explanation of how this inverse was computed?

Here are 5 related questions for further practice:
1. How do you calculate the determinant of a 3x3 matrix?
2. What conditions must a matrix satisfy for its inverse to exist?
3. How do row operations relate to finding a matrix's inverse?
4. Can you find the inverse of a 2x2 matrix?
5. How do you interpret the inverse of a matrix geometrically?

**Tip:** Always check the determinant before computing the inverse, as a matrix with a determinant of zero does not have an inverse.

Find the inverse of the following matrix: C = [[-1, 2, -1], [1, -3, 1], [1, -6, 2]]

Learn how to find the inverse of the matrix C = [[-1, 2, -1], [1, -3, 1], [1, -6, 2]] with a detailed solution. This problem covers key concepts in linear algebra, including matrix inverses, determinants, and matrix operations. Suitable for advanced high school and college students.

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