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The question asks to find the matrix \( A^3 \) for the given matrix \( A \). Let's first extract the matrix \( A \) and compute \( A^3 \).

Matrix \( A \) is given as:

\[
A = \begin{bmatrix} 3 & 1 \\ 2 & -2 \end{bmatrix}
\]

To calculate \( A^3 \), we first find \( A^2 \), then multiply that result by \( A \) again.

Let me calculate that for you.The matrix \( A^3 \) is:

\[
A^3 = \begin{bmatrix} 35 & 9 \\ 18 & -10 \end{bmatrix}
\]

This matches option **D** from the choices provided.

Do you need any further details or clarification?

Here are 5 related questions:
1. How do we calculate the determinant of a 2x2 matrix?
2. What is the inverse of matrix \( A \), if it exists?
3. How can you use eigenvalues and eigenvectors to compute powers of matrices?
4. What is the trace of a matrix, and what is its significance?
5. How does matrix multiplication differ from scalar multiplication?

**Tip:** When multiplying matrices, always remember that matrix multiplication is not commutative (i.e., \( AB \neq BA \) in general).

Diketahui matriks A = [3  1; 2  -2]. Hasil dari A^3 adalah...

Learn how to compute the third power of a 2x2 matrix A = [3  1; 2  -2] using matrix multiplication. This example demonstrates the steps to calculate A^3 and explains important concepts like matrix multiplication and power rules. Suitable for Grades 10-12.

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