query: Prove that $(AB-BA)^n=0$
positive_passages.docid: 28460
positive_passages.text: Show matrix is nilpotent
negative_passages.docid: 32103
negative_passages.text: Show that for a $2\times 2$ matrix $A^2=0$
negative_passages.docid: 52357
negative_passages.text: If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
negative_passages.docid: 151806
negative_passages.text: Prove that $A^k = 0 $ iff $A^2 = 0$
negative_passages.docid: 78298
negative_passages.text: On the nilpotence of the matrix $AB-BA$
negative_passages.docid: 89279
negative_passages.text: If $\sum a_n/k^n = 0$ for all $k$, then $a_n = 0$ for all $n$
negative_passages.docid: 88349
negative_passages.text: Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
negative_passages.docid: 33052
negative_passages.text: How to prove $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime
negative_passages.docid: 26570
negative_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 147014
negative_passages.text: Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$
negative_passages.docid: 131844
negative_passages.text: When does $(e^a)^b = e^{ab}$ hold?
negative_passages.docid: 88995
negative_passages.text: Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
negative_passages.docid: 41411
negative_passages.text: How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$
negative_passages.docid: 19046
negative_passages.text: Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
negative_passages.docid: 64108
negative_passages.text: how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
negative_passages.docid: 30569
negative_passages.text: Prove that the only operator on $\mathbb{C}$ for which his inner product is zero is zero
negative_passages.docid: 12954
negative_passages.text: Prove if $ac>bc$ and $c>0$, then $a>b$