https://file.aiquickdraw.com/mathbot/file/1729752324976udbph40i.jpg

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!

Determine determinant, inverse, and find matrices based on provided equations involving matrix multiplication and inverse.

Solve matrix problems involving determinants, inverses, and equations. Learn the determinant and inverse of a 2x2 matrix and use matrix multiplication to solve for unknown matrices. Suitable for high school students.

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