https://file.aiquickdraw.com/mathbot/file/1729067914234elerfyjv.jpg

In the image, there are two main mathematical expressions:

1. A matrix multiplication problem:
   \[
   \left(\begin{matrix}
   1 & 2 \\
   -1 & 5
   \end{matrix}\right)
   \times 2x2
   \]

2. A matrix \( c \):
   \[
   c = \left(\begin{matrix}
   -1 & 5 & 6 \\
   -6 & 8 & 15
   \end{matrix}\right)
   \]

There is also a linear algebra equation:
\[
\text{Jika } AX = B \text{ maka } X = A^{-1}B
\]
This translates to: If \( AX = B \), then \( X = A^{-1}B \), indicating that if a matrix equation \( AX = B \) is given, the solution for \( X \) can be found using the inverse of \( A \).

Here’s the breakdown of each part:

### 1. Matrix multiplication problem:
You are asked to multiply the 2x2 matrix \( A = \left(\begin{matrix} 1 & 2 \\ -1 & 5 \end{matrix}\right) \) with another 2x2 matrix (possibly \( B \), but it’s not specified in the image). Let me know if you have the second matrix to complete the operation.

### 2. The Matrix \( c \):
This matrix is given as:
\[
c = \left(\begin{matrix}
-1 & 5 & 6 \\
-6 & 8 & 15
\end{matrix}\right)
\]
It is a 2x3 matrix, but it isn’t immediately clear how this relates to the first matrix problem.

### 3. Equation \( AX = B \):
This involves finding \( X \) in the equation \( AX = B \) by calculating \( X = A^{-1}B \). This requires the inverse of matrix \( A \), assuming the matrix \( B \) is provided.

---

Would you like me to calculate the inverse of \( A \) and work through the matrix equation for \( X \)? Or should I solve the multiplication first?

### Questions for further exploration:
1. What is the second matrix in the first multiplication problem?
2. Would you like me to compute the inverse of the matrix \( A \)?
3. Do you want to solve for \( X \) in the matrix equation \( AX = B \)?
4. How does matrix \( c \) relate to the rest of the problem?
5. Is there additional context for how the equation \( X = A^{-1}B \) should be used here?

#### Tip:
When solving for \( X \) in matrix equations, it's important to check if the matrix \( A \) is invertible by ensuring its determinant is non-zero.

Solve the given matrix problem involving multiplication and the equation AX = B. Matrices A and C are given, with a hint that X = A⁻¹B.

Explore how to multiply matrices and solve the linear equation AX = B using matrix inverses. This problem covers key linear algebra concepts, including matrix multiplication and inversion. Suitable for students at the advanced high school or undergraduate level.

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