If $A = \begin{bmatrix}2 & k \\ 1 & 3\end{bmatrix}$, $B = \begin{bmatrix}3 & -6 \\ -1 & 2\end{bmatrix}$ and $AB = O$, what is $k$?

Explanation

1. 01

   Row 1 of $A$ times column 1 of $B$: $2(3) + k(-1) = 6 - k$, which must be 0.

2. 02

   So $k = 6$, and the other three elements, $-12 + 2k$, $3 - 3$ and $-6 + 6$, are 0 as well. Neither $A$ nor $B$ is $O$, yet $AB = O$.