Let $A$ be an $n \times n$ matrix for which $A^k = 0$ for some $k > n$. Show that $A^n = 0$.
41411
How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$
140400
Prove normal matrix is 4th power of some self-adjoint matrix
149287
Prove that $A,B>0$ and $A_{ij}0$
157847
If $x_n \to 0$, show that $\sqrt{x_n} \to 0$
75002
show that $\det(A)=0$ in this case
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
118283
Show that if $A^{n}=I$ then $A$ is diagonalizable.
111550
Let $A$ be a square complex matrix of size $n$ then $\langle Ax,x\rangle=0$ for $\forall x \in \Bbb C^n$ $\iff A=0$
151806
Prove that $A^k = 0 $ iff $A^2 = 0$
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
21758
Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal
25488
Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
153506
Proving the inverse of a matrix equals $I_n-\frac{1}{n-1}A$
7843
Show that order of $a^k$
25682
If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
1973
Traces of all positive powers of a matrix are zero implies it is nilpotent
106398
If $A$ is invertible show that $\det(A) \neq 0$