1.2. Given matrices

1) $A=\left(\begin{array}{lll}1 & 1 & 2 \\ 3 & 2 & 3 \\ 4 & 3 & 2\end{array}\right), B=\left(\begin{array}{cc}1 & 1 \\ -1 & 2 \\ 1 & 4\end{array}\right)$;
2) $A=\left(\begin{array}{lll}1 & 1 & 3 \\ 1 & 0 & 2\end{array}\right), B=\left(\begin{array}{ccc}1 & 3 & 2 \\ 1 & 0 & 2 \\ 1 & 0 & -1\end{array}\right)$.

Find $A \cdot B$.
Solution. According to the definition of matrix multiplication, we have:

$$
\text { 1) } A \cdot B=\left(\begin{array}{ll}
1 \cdot 1+1 \cdot(-1)+2 \cdot 1 & 1 \cdot 1+1 \cdot 2+2 \cdot 4 \\
3 \cdot 1+2 \cdot(-1)+3 \cdot 1 & 3 \cdot 1+2 \cdot 2+3 \cdot 4 \\
4 \cdot 1+3 \cdot(-1)+2 \cdot 1 & 4 \cdot 1+3 \cdot 2+2 \cdot 4
\end{array}\right)=\left(\begin{array}{ll}
2 & 11 \\
4 & 19 \\
3 & 18
\end{array}\right)
$$

2) $A \cdot B=\left(\begin{array}{lll}1 \cdot 1+1 \cdot 1+3 \cdot 1 & 1 \cdot 3+1 \cdot 0+1 \cdot 0 & 1 \cdot 2+1 \cdot 2+3 \cdot(-1) \\ 1 \cdot 1+0 \cdot 1+2 \cdot 1 & 1 \cdot 3+0 \cdot 0+2 \cdot 0 & 1 \cdot 2+0 \cdot 2+2 \cdot(-1)\end{array}\right)=\left(\begin{array}{lll}5 & 3 & 1 \\ 3 & 3 & 0\end{array}\right)$.