Prove that if $A^2=0$, then $0$ is the only eigenvalue of $A$.
10001
Prove that the only eigenvalue of a nilpotent operator is 0?
73677
If the matrix $A^3 = 0$, is $A$ singular?
104293
How to prove "eigenvalues of polynomial of matrix $A$ = polynomial of eigenvalues of matrix $A$ "
118467
Prove that $a^2+ab+b^2\ge 0$
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
19649
A question about the proof of "a symmetric matrix has real eigenvalues".
158205
If $A+A^T$ is negative definite, then the eigenvalues of $A$ have negative real parts?
52928
If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
98541
If a Matrix Has Only Zero as an Eigen-Value Then It Is Nilpotent
9220
If $\lambda$ is an eigenvalue of $A^2$, then either $\sqrt{\lambda}$ or $-\sqrt{\lambda}$ is an eigenvalue of $A$
44596
If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.
111550
Let $A$ be a square complex matrix of size $n$ then $\langle Ax,x\rangle=0$ for $\forall x \in \Bbb C^n$ $\iff A=0$
80022
Eigenvector of A by $A^2$
76110
Proving that the zero vector is unique
118283
Show that if $A^{n}=I$ then $A$ is diagonalizable.
153203
Let $4$ and $5$ be the only eigenvalues of $T$. Show $T^2-9T + 20I = 0$ , T is self adjoint.
3433
Proof if $a \vec v = 0$ then $a = 0$ or $\vec v = 0$