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You have provided a matrix \( A = \begin{pmatrix} 1 & 3 \\ 4 & 5 \end{pmatrix} \).

Let me know if you'd like me to solve or perform any operations with this matrix, such as finding its determinant, inverse, eigenvalues, or solving a system of equations involving this matrix. 

Would you like more details or have any questions? Here are some follow-up ideas:

1. What is the determinant of matrix \( A \)?
2. How do you calculate the inverse of a 2x2 matrix?
3. What are the eigenvalues and eigenvectors of matrix \( A \)?
4. Can you perform matrix multiplication involving matrix \( A \)?
5. How would this matrix transform a vector in \( \mathbb{R}^2 \)?

**Tip:** When working with 2x2 matrices, the determinant is a key factor in determining whether the matrix is invertible or singular.

What operations can be performed with matrix A = [[1, 3], [4, 5]]?

Learn how to calculate the determinant, inverse, and eigenvalues for the 2x2 matrix A = [[1, 3], [4, 5]]. This guide covers important matrix operations and provides detailed steps for solving these concepts in linear algebra. Suitable for high school and early university students.

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