Matrix multiplication/Upper triangular matrix/4/Zero diagonal/Nilpotent/Exercise

We consider the matrix

${}M={\begin{pmatrix}0&a&b&c\\0&0&d&e\\0&0&0&f\\0&0&0&0\end{pmatrix}}\,$

over a field ${}K$. Show that the fourth power of ${}M$ is ${}0$, that is

${}M^{4}=MMMM=0\,.$

Create a solution