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The problem asks to find the result of the multiplication of two matrices:

\[
\begin{pmatrix} 1 & 3 \\ -2 & 2 \end{pmatrix} \cdot \begin{pmatrix} -3 & 5 \\ 4 & -2 \end{pmatrix}
\]

### Step-by-Step Matrix Multiplication:
Let the two matrices be:
\[
A = \begin{pmatrix} 1 & 3 \\ -2 & 2 \end{pmatrix}, \quad B = \begin{pmatrix} -3 & 5 \\ 4 & -2 \end{pmatrix}
\]

To multiply \(A\) and \(B\), we compute each element of the resulting matrix \(C = A \cdot B\) as follows:

\[
C_{ij} = A_{i1} \cdot B_{1j} + A_{i2} \cdot B_{2j}
\]

For the element at position (1,1):
\[
C_{11} = (1 \cdot -3) + (3 \cdot 4) = -3 + 12 = 9
\]

For the element at position (1,2):
\[
C_{12} = (1 \cdot 5) + (3 \cdot -2) = 5 - 6 = -1
\]

For the element at position (2,1):
\[
C_{21} = (-2 \cdot -3) + (2 \cdot 4) = 6 + 8 = 14
\]

For the element at position (2,2):
\[
C_{22} = (-2 \cdot 5) + (2 \cdot -2) = -10 - 4 = -14
\]

### Final Result:
\[
C = \begin{pmatrix} 9 & -1 \\ 14 & -14 \end{pmatrix}
\]

The correct result of the matrix multiplication is:

\[
\boxed{\begin{pmatrix} 9 & -1 \\ 14 & -14 \end{pmatrix}}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you multiply two matrices in general?
2. What is the determinant of matrix \( A \) and \( B \)?
3. Can matrix multiplication be commutative (i.e., \( A \cdot B = B \cdot A \))?
4. How does matrix multiplication relate to solving systems of equations?
5. What is the difference between matrix multiplication and the Hadamard (element-wise) product?

### Tip:
Matrix multiplication is not commutative, meaning \( A \cdot B \neq B \cdot A \) in most cases. Always verify the order of multiplication!

Hasil yang tepat untuk perkalian matriks \begin{pmatrix} 1 & 3 \\ -2 & 2 \end{pmatrix} \cdot \begin{pmatrix} -3 & 5 \\ 4 & -2 \end{pmatrix} adalah ...

Find the exact result of multiplying two 2x2 matrices \begin{pmatrix} 1 & 3 \\ -2 & 2 \end{pmatrix} and \begin{pmatrix} -3 & 5 \\ 4 & -2 \end{pmatrix}. A step-by-step matrix multiplication guide, involving key linear algebra concepts.

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