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The problem asks to find the result of \( A^2 \cdot B^T \), where matrices \( A \) and \( B \) are given, and \( B^T \) is the transpose of matrix \( B \). Let's break it down:

Given matrices:
\[ A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} -1 & 1 \\ 2 & -2 \\ -3 & 3 \end{pmatrix} \]

1. **Step 1: Compute \( A^2 \)**

   \( A^2 \) is found by multiplying matrix \( A \) by itself:
   \[
   A^2 = A \cdot A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \cdot \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}
   \]
   Perform matrix multiplication to get \( A^2 \).

2. **Step 2: Compute the transpose of \( B \)**
   
   The transpose of matrix \( B \), denoted \( B^T \), is obtained by swapping rows with columns:
   \[
   B^T = \begin{pmatrix} -1 & 2 & -3 \\ 1 & -2 & 3 \end{pmatrix}
   \]

3. **Step 3: Multiply \( A^2 \) with \( B^T \)**

   After finding \( A^2 \) and \( B^T \), multiply them together:
   \[
   A^2 \cdot B^T
   \]
   Perform matrix multiplication to get the result.

I will now calculate these steps.

Diketahui matriks A = [[1, 2], [3, 4]] dan matriks B = [[-1, 1], [2, -2], [-3, 3]] serta B^T adalah transpos dari matriks B. Hasil dari A^2 * B^T adalah...

Solve a matrix multiplication problem involving A^2 and B^T, where matrices A = [[1, 2], [3, 4]] and B = [[-1, 1], [2, -2], [-3, 3]]. This solution involves calculating the square of matrix A and the transpose of matrix B, followed by their multiplication. Suitable for Grades 11-12 or undergraduate linear algebra students.

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