If $A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$ and $B = \begin{bmatrix}2 & 0 \\ 1 & 3\end{bmatrix}$, what is $AB$?

Explanation

1. 01

   Each element of $AB$ is a row of $A$ times a column of $B$, entry by entry, added up.

2. 02

   For example, row 1 times column 1: $(1)(2) + (2)(1) = 4$.

3. 03

   So $AB = \begin{bmatrix}4 & 6 \\ 10 & 12\end{bmatrix}$.