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The inverse of matrix \( A \) is:

\[
A^{-1} = \begin{pmatrix}
0.0126 & -0.0103 & 0.0032 & -0.0017 \\
0.0678 & -0.0573 & -0.0040 & 0.0114 \\
-0.0664 & 0.1990 & -0.0084 & -0.0584 \\
0.0395 & -0.0743 & 0.0112 & 0.0696
\end{pmatrix}
\]

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Here are some related questions you could explore:
1. What conditions must be met for a matrix to have an inverse?
2. How do you compute the determinant of matrix \( A \)?
3. How can matrix inverses be used to solve systems of linear equations?
4. What is the geometric interpretation of a matrix inverse?
5. How does the inverse of a product of matrices relate to the individual inverses?

**Tip:** A matrix must be square and its determinant must be non-zero to have an inverse.

This tutorial walks you through the process of finding the inverse of a 4x4 matrix A, including how to calculate the determinant and adjugate matrix. Understand the key mathematical concepts involved, such as the Invertible Matrix Theorem, and learn the formulas for matrix inversion. Ideal for university-level linear algebra students.

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