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The problem involves multiplying two matrices. Let me walk through the solution.

We have the following matrices to multiply:

\[
\begin{pmatrix}
3 & -2 \\
-3 & -1 \\
2 & 3
\end{pmatrix}
\cdot
\begin{pmatrix}
-1 & 2 \\
-2 & 3
\end{pmatrix}
\]

This is a matrix multiplication problem. The result will be a \(3 \times 2\) matrix, since we are multiplying a \(3 \times 2\) matrix by a \(2 \times 2\) matrix. The elements of the resulting matrix are obtained by taking the dot products of the rows of the first matrix with the columns of the second matrix.

### Step 1: Calculate the elements of the resulting matrix.

1. **Element (1,1):**
\[
(3 \cdot -1) + (-2 \cdot -2) = -3 + 4 = 1
\]

2. **Element (1,2):**
\[
(3 \cdot 2) + (-2 \cdot 3) = 6 - 6 = 0
\]

3. **Element (2,1):**
\[
(-3 \cdot -1) + (-1 \cdot -2) = 3 + 2 = 5
\]

4. **Element (2,2):**
\[
(-3 \cdot 2) + (-1 \cdot 3) = -6 - 3 = -9
\]

5. **Element (3,1):**
\[
(2 \cdot -1) + (3 \cdot -2) = -2 - 6 = -8
\]

6. **Element (3,2):**
\[
(2 \cdot 2) + (3 \cdot 3) = 4 + 9 = 13
\]

### Final Answer:

The resulting matrix is:
\[
\begin{pmatrix}
1 & 0 \\
5 & -9 \\
-8 & 13
\end{pmatrix}
\]

Would you like further details on the steps or have any other questions?

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Here are 5 related questions:

1. What is the general rule for matrix multiplication?
2. Can two matrices of any size always be multiplied? Why or why not?
3. How would the result differ if the matrices were square (e.g., \(2 \times 2\))?
4. What happens when you multiply a matrix by its inverse?
5. How do you compute the determinant of a matrix?

**Tip:** When multiplying matrices, make sure the number of columns in the first matrix matches the number of rows in the second matrix to ensure the operation is defined.

Multiply the matrices: [[3, -2], [-3, -1], [2, 3]] and [[-1, 2], [-2, 3]].

Learn how to multiply a 3x2 matrix with a 2x2 matrix step-by-step. This detailed solution explains the matrix multiplication process, covering key linear algebra concepts suitable for advanced high school or undergraduate students.

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