Is a zero matrix nilpotent matrix? Let a matrix $A=0$. Can I say $A$ is nilpotent? I am asking if the zero matrix is nilpotent or not.
Nilpotent means that $A^k = 0$ for some $k$ that is a non-negative integer. When $k = 1$, $A^k = A = 0$. Does this idea support that a zero matrix is nilpotent?
Sure, the zero matrix $0$ is nilpotent since any of its powers is again the zero matrix.
Just a side note: This question would be more suitable at the math stackexchange.