Question

Give examples of matrices

 A and B such that AB = O but A ≠ 0, B ≠ 0.

Answer 1

\[\left( ii \right) Let A = \begin{bmatrix}0 & 2 \\ 0 & 0\end{bmatrix} and B = \begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix}\]

\[ \therefore AB = \begin{bmatrix}0 + 0 & 0 + 0 \\ 0 + 0 & 0 + 0\end{bmatrix} = \begin{bmatrix}0 & 0 \\ 0 & 0\end{bmatrix} = O\]

Thus, AB = O while A ≠ 0 and B ≠ 0.