Question

Given an example of two non-zero 2 × 2 matrices A and B such that AB = O.

 

Answer 1

Let the two matrices be A = \begin{bmatrix}5 & 0 \\ 9 & 0\end{bmatrix} and B = \begin{bmatrix}0 & 0 \\ 12 & - 21\end{bmatrix}, such that AB = \begin{bmatrix}5 & 0 \\ 9 & 0\end{bmatrix}\begin{bmatrix}0 & 0 \\ 12 & - 21\end{bmatrix} 

\[ \Rightarrow AB = \begin{bmatrix}0 & 0 \\ 0 & 0\end{bmatrix}\]