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To solve the given problem, we need to find the inverse of the matrix \( A \) using row operations. The matrix \( A \) is:

\[
A = \begin{pmatrix}
1 & -1 & -1 \\
0 & -2 & -1 \\
-2 & -3 & 0
\end{pmatrix}
\]

### Steps to find the inverse of matrix \( A \):

1. **Form the augmented matrix \( [A | I] \)**: 
   We augment matrix \( A \) with the identity matrix of the same size (3x3). So the augmented matrix looks like this:

   \[
   [A | I] = \begin{pmatrix}
   1 & -1 & -1 & | & 1 & 0 & 0 \\
   0 & -

Find A^-1 by forming [A | I] and then using row operations to obtain [I | B], where A^-1 = [B]. Check that AA^-1 = I and A^-1 A = I.

Learn how to find the inverse of a matrix using row operations. This example guides you through forming the augmented matrix [A | I] and applying row reductions to obtain the inverse matrix. Suitable for undergraduate linear algebra students.

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