Show that if $A$ is a nilpotent matrix then there exists $k\leq n$ s.t. $A^k=0$ without using Cayley-Hamilton
41411
How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$
75104
Existence of some type matrix
119452
Nilpotent matrices with same minimal polynomial and nullity
115273
Nilpotent matrix and basis for $F^n$
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
34908
$A$ is normal and nilpotent, show $A=0$
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
94406
Degree of minimum polynomial at most $n$ without Cayley-Hamilton?
97487
How to prove whether a matrix has rank $1$
35155
To prove Cayley-Hamilton theorem, why can't we substitute $A$ for $\lambda$ in $p(\lambda) = \det(\lambda I - A)$?
57296
A non-diagonal $4\times4$ matrix such that $A^3=A^2=0$ and its rank is $2$
94639
Proof that the rank of a skew-symmetric matrix is at least $2$
158426
Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
6514
Prove $T$ has at most two distinct eigenvalues
55272
Prove that all nxn nilpotent matrices of order n are similar.
31766
Prove that $a_{n}=0$ for all $n$, if $\sum a_{kn}=0$ for all $k\geq 1$
120933
A is similar to $A^k$, then each eigenvalue of $A$ is a root of unity