Let $A$ be a $10\times 10$ matrix and $A^{10,000} = 0$ Show $A^{10} = 0$
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
57296
A non-diagonal $4\times4$ matrix such that $A^3=A^2=0$ and its rank is $2$
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
51800
We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$
151806
Prove that $A^k = 0 $ iff $A^2 = 0$
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
66451
In a ring, how do we prove that a * 0 = 0?
4517
Showing a $2\times2$ matrix is invertible
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
124090
zero matrix to the power of 0
126018
Show that $ e^{A+B}=e^A e^B$
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
37252
How can I show that $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}^n = \begin{pmatrix} 1 & n \\ 0 & 1\end{pmatrix}$?
100627
for a $3 \times 3$ matrix A ,value of $ A^{50} $ is
41411
How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$
66861
Show that $11^{10} \equiv 1 (\mod 100)$
34908
$A$ is normal and nilpotent, show $A=0$