Multiply the Symmetric Matrix A by the Skew-Symmetric Matrix B
[latex] \[
\textbf{Multiply the Symmetric Matrix A by the Skew-Symmetric Matrix B, where:}
\]
\[
A = \begin{pmatrix} 2 & 1 \\ 1 & 3 \end{pmatrix}, \quad B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}
\]
\[
\textbf{Solution:}
\]
\[
A \times B = \begin{pmatrix} 2 & 1 \\ 1 & 3 \end{pmatrix} \times \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}
\]
\[
= \begin{pmatrix} (2 \cdot 0 + 1 \cdot -1) & (2 \cdot 1 + 1 \cdot 0) \\ (1 \cdot 0 + 3 \cdot -1) & (1 \cdot 1 + 3 \cdot 0) \end{pmatrix}
\]
\[
= \begin{pmatrix} -1 & 2 \\ -3 & 1 \end{pmatrix}
\]