Multiply Matrix A (3×3) by Matrix B (3×2)

[latex] \[
\textbf{Multiply Matrix A (3×3) by Matrix B (3×2), where:}
\]
\[
A = \begin{pmatrix} 1 & 0 & 2 \\ -1 & 3 & 1 \\ 2 & 2 & 0 \end{pmatrix}, \quad B = \begin{pmatrix} 3 & 1 \\ 2 & 4 \\ 1 & 0 \end{pmatrix}
\]
\[
\textbf{Solution:}
\]
\[
A \times B = \begin{pmatrix} 1 & 0 & 2 \\ -1 & 3 & 1 \\ 2 & 2 & 0 \end{pmatrix} \times \begin{pmatrix} 3 & 1 \\ 2 & 4 \\ 1 & 0 \end{pmatrix}
\]
\[
= \begin{pmatrix}
(1 \cdot 3 + 0 \cdot 2 + 2 \cdot 1) & (1 \cdot 1 + 0 \cdot 4 + 2 \cdot 0) \\
(-1 \cdot 3 + 3 \cdot 2 + 1 \cdot 1) & (-1 \cdot 1 + 3 \cdot 4 + 1 \cdot 0) \\
(2 \cdot 3 + 2 \cdot 2 + 0 \cdot 1) & (2 \cdot 1 + 2 \cdot 4 + 0 \cdot 0)
\end{pmatrix}
\]
\[
= \begin{pmatrix} 5 & 1 \\ 4 & 11 \\ 10 & 10 \end{pmatrix}
\]