https://file.aiquickdraw.com/mathbot/file/17271187598673udefrhj.jpg

It seems that there was an issue processing the Russian text from the image. I will focus on solving the matrix problems directly from the image content, based on the given matrices.

Let me solve each of the matrix multiplication tasks:

1. **Task 1.1.6**:  
   \[
   A = \begin{pmatrix} 3 & -2 \\ 5 & -4 \end{pmatrix}, \quad B = \begin{pmatrix} 3 & 4 \\ 2 & 5 \end{pmatrix}
   \]
   Find \( AB \) and \( BA \).

2. **Task 1.1.7**:  
   \[
   A = \begin{pmatrix} 4 & 0 \\ -2 & 3 \\ 1 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} 3 \\ 1 \\ -1 \\ 5 \\ 2 \end{pmatrix}
   \]
   Find \( AB \).

3. **Task 1.1.8**:  
   \[
   A = \begin{pmatrix} 1 & 2 \\ 3 & 6 \end{pmatrix}, \quad B = \begin{pmatrix} 2 & 6 \\ -1 & -3 \end{pmatrix}
   \]
   Find \( AB \) and \( BA \).

4. **Task 1.1.9**:  
   \[
   A = \begin{pmatrix} 2 & 1 \\ 5 & 3 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & 3 \\ 5 & 2 \end{pmatrix}
   \]
   Find \( AB \) and \( BA \).

5. **Task 1.1.10**:  
   \[
   A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & 3 \\ -2 & 2 \end{pmatrix}
   \]
   Find \( AB \) and \( BA \).

I will solve each of these matrix multiplication problems step by step. Let's begin with 1.1.6.For **Task 1.1.6**, the results are:

\[
AB = \begin{pmatrix} 5 & 2 \\ 7 & 0 \end{pmatrix}, \quad BA = \begin{pmatrix} 29 & -22 \\ 31 & -24 \end{pmatrix}
\]

Now let's proceed to solve **Task 1.1.7**.For **Task 1.1.7**, the result of the matrix multiplication is:

\[
AB = \begin{pmatrix} 12 \\ -3 \\ 4 \end{pmatrix}
\]

Next, let's solve **Task 1.1.8**.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can continue solving the matrix multiplication manually or explain the concepts behind the operations. Let me know how you'd like to proceed!

Would you like further details or have any questions? Here are some related questions you might find useful:

1. How do you determine if matrix multiplication is valid?
2. What are the properties of matrix multiplication?
3. What is the significance of the order of multiplication for matrices?
4. Can you explain how to compute determinants for 2x2 matrices?
5. How do matrix operations change when using non-square matrices?

**Tip**: When multiplying matrices, always check the dimensions to ensure that the number of columns in the first matrix matches the number of rows in the second matrix.

Find the product of matrices AB and BA for the given matrix pairs.

Explore how to multiply matrices and find the products AB and BA for different pairs of matrices. This problem covers core linear algebra concepts such as matrix multiplication and its properties. Learn step-by-step how to check if matrix multiplication is valid and compute the product.

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