Prove that a square matrix over an algebraic closed field is nilpotent if and only if all their eigenvalues are zero.
37867
If $0$ is the only eigenvalue of a linear operator, is the operator nilpotent
158426
Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
133758
Traces of powers of a matrix $A$ over an algebra are zero implies $A$ nilpotent.
144898
Let $A$ be complex matrix and $x$ be eigenvalue of $A\overline{A}$. Algebraic multiplicity of $x$ is even.
19649
A question about the proof of "a symmetric matrix has real eigenvalues".
55272
Prove that all nxn nilpotent matrices of order n are similar.
94639
Proof that the rank of a skew-symmetric matrix is at least $2$
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
1973
Traces of all positive powers of a matrix are zero implies it is nilpotent
34908
$A$ is normal and nilpotent, show $A=0$
66968
if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent
107128
Let $B$ be a nilpotent $n\times n$ matrix with complex entries let $A = B-I$ then find $\det(A)$
28460
Show matrix is nilpotent
13346
If $A=AB-BA$, is $A$ nilpotent?
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
41932
Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
115782
Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz