A matrix with the property $\mathrm{tr}(A^{m})=0$ for every $m$ is nilpotent?
1973
Traces of all positive powers of a matrix are zero implies it is nilpotent
132366
Diagonalizability of $A \in M_{n}(\Bbb{R})$ (Upper traingular matrix) with all diagonal entries 1 and $A \neq I$?
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
28460
Show matrix is nilpotent
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
119452
Nilpotent matrices with same minimal polynomial and nullity
61868
Prove that $ND = DN$ where $D$ is a diagonalizable and $N$ is a nilpotent matrix.
153119
$x^TAx=0$ for all $x$ when $A$ is a skew symmetric matrix
120407
Is every noninvertible matrix a zero divisor?
134402
$\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
12596
Show that $f(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n\in R[x]$ is nilpotent iff $a_0,a_1,a_2,\ldots,a_n$ are nilpotent
115296
Under what conditions does a matrix $A$ have a square root?
140252
Matrices - Conditions for $AB+BA=0$
44898
Help with commutative property of matrices problem
33611
necessary and sufficient condition for trivial kernel of a matrix over a commutative ring
71040
If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?