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.