The image contains four matrix problems. Here's a breakdown of each problem:

1. Determine the determinant of $A \times B$, where: $A = \begin{pmatrix} 2 & 5 \\ 4 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} 3 & 1 \\ -1 & 2 \end{pmatrix}$

2. Find the inverse of $A + B$, where: $A = \begin{pmatrix} 7 & 5 \\ 4 & 2 \end{pmatrix}, \quad B = \begin{pmatrix} -3 & 2 \\ 1 & 2 \end{pmatrix}$

3. Given that $X \times A = B$, find matrix $X$, where: $A = \begin{pmatrix} 4 & -5 \\ -2 & 2 \end{pmatrix}, \quad B = \begin{pmatrix} -1 & 6 \\ 1 & -3 \end{pmatrix}$

4. If $X \times A = B$, find matrix $X$, where: $A = \begin{pmatrix} -4 & -6 \\ 2 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} 3 & 2 \\ 1 & 1 \end{pmatrix}$

Would you like a detailed solution for each question or a specific one? Let me know!

Here are five related questions:

1. What is the determinant of matrix $B$ individually in problem 1?
2. How do you compute the inverse of a matrix in general?
3. What methods can be used to solve $X \times A = B$?
4. What is the sum of matrices $A$ and $B$ in problem 2?
5. Can you describe a case where matrix multiplication is not commutative?

Tip: When solving matrix equations like $X \times A = B$, multiplying both sides by the inverse of matrix $A$ is often useful!