$A$ is defined as an $m\times m$ matrix which is not invertible. How can i show that there is an $m\times m$ matrix $B$ where $AB = 0$ but $B$ is not equal to $0$?
For the solution of this question I think giving an example is not enough because it is too easy to solve this by giving an example, so how can I show that $B$ is not the $0$ matrix?