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The question asks which pair of matrices can be multiplied. In matrix multiplication, two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Let’s analyze each pair of matrices from the options:

1. **Option A**:
   - First matrix: \( \begin{pmatrix} -1 \\ \frac{3}{2} \end{pmatrix} \) (size: 2 rows × 1 column)
   - Second matrix: \( \begin{pmatrix} 1 & 2 \\ 2 & -1 \end{pmatrix} \) (size: 2 rows × 2 columns)
   
   The first matrix has 1 column, and the second matrix has 2 rows. Since the number of columns in the first matrix is not equal to the number of rows in the second matrix, these matrices **cannot be multiplied**.

2. **Option B**:
   - First matrix: \( \begin{pmatrix} 1 & 5 \end{pmatrix} \) (size: 1 row × 2 columns)
   - Second matrix: \( \begin{pmatrix} 1 & -2 & 3 \\ -1 & 2 & 4 \end{pmatrix} \) (size: 2 rows × 3 columns)
   
   The first matrix has 2 columns, and the second matrix has 2 rows. Since the number of columns in the first matrix equals the number of rows in the second matrix, these matrices **can be multiplied**.

3. **Option C**:
   - First matrix: \( \begin{pmatrix} 2 & -1 \\ -1 & 4 \end{pmatrix} \) (size: 2 rows × 2 columns)
   - Second matrix: \( \begin{pmatrix} 0 \\ 1 \\ -\frac{1}{2} \\ -2 \end{pmatrix} \) (size: 4 rows × 1 column)
   
   The first matrix has 2 columns, and the second matrix has 4 rows. Since the number of columns in the first matrix is not equal to the number of rows in the second matrix, these matrices **cannot be multiplied**.

4. **Option D**:
   - First matrix: \( \begin{pmatrix} 2 & 1 \end{pmatrix} \) (size: 1 row × 2 columns)
   - Second matrix: \( \begin{pmatrix} 2 & 1 & 0 \\ 3 & 1 & 0 \end{pmatrix} \) (size: 2 rows × 3 columns)
   
   The first matrix has 2 columns, and the second matrix has 2 rows. Since the number of columns in the first matrix equals the number of rows in the second matrix, these matrices **can be multiplied**.

5. **Option E**:
   - First matrix: \( \begin{pmatrix} 1 & 0 & -5 \\ 4 & -2 & 3 \\ -1 & 2 & 4 \end{pmatrix} \) (size: 3 rows × 3 columns)
   - Second matrix: \( \begin{pmatrix} 4 & 3 \\ 2 & 1 \\ 3 & 0 \end{pmatrix} \) (size: 3 rows × 2 columns)
   
   The first matrix has 3 columns, and the second matrix has 3 rows. Since the number of columns in the first matrix equals the number of rows in the second matrix, these matrices **can be multiplied**.

### Conclusion:
- Correct answers: **B, D, E** are the pairs of matrices that can be multiplied.

Do you need a detailed solution for any specific matrix multiplication?

Here are 5 related questions to expand your understanding:
1. How do you multiply two matrices step by step?
2. What is the condition for matrix multiplication to be valid?
3. Can matrix multiplication be performed in any order?
4. What are the properties of the identity matrix in matrix multiplication?
5. How do you calculate the determinant of a matrix?

**Tip:** Always verify the dimensions of the matrices before attempting multiplication.

Pasangan matriks berikut yang dapat dikalikan adalah ...

This problem asks which pairs of matrices can be multiplied based on their dimensions. The solution provides a detailed analysis of each matrix pair, using matrix multiplication rules. Suitable for high school students in Grades 10-12.

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