If $A = \begin{bmatrix}2 & -1 \\ 0 & 3\end{bmatrix}$ and $B = \begin{bmatrix}1 & 4 \\ 2 & -2\end{bmatrix}$, 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: $(2)(1) + (-1)(2) = 0$.

3. 03

   So $AB = \begin{bmatrix}0 & 10 \\ 6 & -6\end{bmatrix}$.