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To solve for the determinant of \( A \times B \), where:

\[
A = \begin{pmatrix} 2 & 5 \\ 1 & 3 \end{pmatrix}, \quad B = \begin{pmatrix} -2 & 5 \\ 2 & -3 \end{pmatrix}
\]

The property of determinants states that:

\[
\text{det}(A \times B) = \text{det}(A) \times \text{det}(B)
\]

### Step 1: Find the determinant of matrix \( A \)
\[
\text{det}(A) = (2 \times 3) - (5 \times 1) = 6 - 5 = 1
\]

### Step 2: Find the determinant of matrix \( B \)
\[
\text{det}(B) = (-2 \times -3) - (5 \times 2) = 6 - 10 = -4
\]

### Step 3: Calculate the determinant of \( A \times B \)
\[
\text{det}(A \times B) = \text{det}(A) \times \text{det}(B) = 1 \times (-4) = -4
\]

Therefore, the determinant of \( A \times B \) is \( -4 \).

The correct answer is **d. -4**.

Would you like more details or have any questions? Here are some related questions for further practice:

1. How do you compute the determinant of a 3x3 matrix?
2. What is the determinant of a diagonal matrix?
3. Can a matrix with a zero determinant be inverted?
4. How does the determinant change when two rows of a matrix are swapped?
5. What are the properties of the determinant in relation to matrix multiplication?

**Tip:** The determinant of a product of two matrices is always the product of their individual determinants.

Jika A = \( \begin{pmatrix} 2 & 5 \\ 1 & 3 \end{pmatrix} \) dan B = \( \begin{pmatrix} -2 & 5 \\ 2 & -3 \end{pmatrix} \), maka determinan A x B adalah ....

Learn how to calculate the determinant of the matrix product A x B, where A and B are 2x2 matrices. This solution uses the properties of determinants and covers key concepts from linear algebra. Suitable for students in Grades 10-12.

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