Find two nilpotent 2 by 2 matrices such that their sum is not nilpotent.
I have been trying a few matrices but none are working, is there a more logical, easier way to find these matrices? thanks.
Because if $\displaystyle A$ is invertible then $\displaystyle A^n$ is invertible. Thus, if $\displaystyle A^n$ is not invertible then $\displaystyle A$ is not invertible. If $\displaystyle A^n $ is zero matrix then it means $\displaystyle A^n$ is not invertible and so $\displaystyle A$ is not invertible.