https://file.aiquickdraw.com/mathbot/file/1726711973281i7pcbnmx.jpg

The problem in the image involves multiplying two matrices.

Matrix 1: 
\[
\begin{pmatrix}
1 & 2 \\
-1 & -2 \\
3 & 1
\end{pmatrix}
\]

Matrix 2: 
\[
\begin{pmatrix}
2 & -1 \\
1 & 3
\end{pmatrix}
\]

We will perform matrix multiplication. The result will be a \(3 \times 2\) matrix (since the first matrix is \(3 \times 2\) and the second is \(2 \times 2\)).

Let me compute that for you.The result of multiplying the two matrices is:

\[
\begin{pmatrix}
4 & 5 \\
-4 & -5 \\
7 & 0
\end{pmatrix}
\]

Would you like further explanation on how matrix multiplication works?

Here are 5 related questions to expand your understanding:
1. How is matrix multiplication defined?
2. What are the properties of matrix multiplication (commutativity, associativity, etc.)?
3. What are the applications of matrix multiplication in real-world problems?
4. How can you compute the inverse of a matrix?
5. How is matrix multiplication used in solving systems of linear equations?

**Tip:** Always ensure the inner dimensions of matrices are the same when performing matrix multiplication (i.e., the number of columns in the first matrix must equal the number of rows in the second).

Multiply the matrices:

Matrix 1: 
\(
\begin{pmatrix}
1 & 2 \\
-1 & -2 \\
3 & 1
\end{pmatrix}
\)

Matrix 2: 
\(
\begin{pmatrix}
2 & -1 \\
1 & 3
\end{pmatrix}
\)

Learn how to multiply a 3x2 matrix with a 2x2 matrix, involving key linear algebra concepts. The step-by-step solution shows the computation of each element in the resulting matrix using the matrix multiplication formula.

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