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The matrix \( A \) from problem 37 is invertible since its determinant is \( \det(A) = 2.0 \), which is not zero.

The inverse of matrix \( A \) is:

\[
A^{-1} = \begin{bmatrix}
0.5 & 0.5 & -0.5 \\
-0.5 & 0.5 & 0.5 \\
0.5 & -0.5 & 0.5
\end{bmatrix}
\]

Would you like further details on how the inverse was computed or have any questions?

Here are 5 related questions to expand your understanding:
1. How can you check if a matrix is invertible without calculating the determinant?
2. What is the geometric significance of the determinant of a matrix?
3. Can you find the inverse of a 2x2 matrix manually? If so, how?
4. Why does a determinant of 0 indicate that a matrix is not invertible?
5. What are some applications of matrix inverses in real-world problems?

**Tip**: When a matrix has a determinant of 0, it is called singular, meaning it cannot be inverted.

Determine whether matrix A is invertible, and if so, find the inverse for the matrix A = [[1, 0, 1], [1, 1, 0], [0, 1, 1]].

Learn how to determine whether a 3x3 matrix is invertible and how to find its inverse. In this problem, matrix A is tested for invertibility using its determinant and then inverted using standard linear algebra techniques. Ideal for students studying matrix operations in linear algebra.

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