How to prove that there aren't square matrices $A$ and $B$, such as $AB - BA = I_n$
7622
$AB-BA=I$ having no solutions
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
104653
$A$ and $B$ are $3\times 3$ real matrices such that $\operatorname{rank}(AB)=1$, then $\operatorname{rank}(BA$) can not be which of the following?
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
12189
Prove norm doesn't come from inner product.
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
25682
If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
73155
Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
25488
Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
6091
Similarity of products $AB$ and $BA$ of square matrices
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
84422
$AB=BA$, $AC=CA$ we need to show $BC=CB$
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
3301
If $AB = I$ then $BA = I$
3330
Square matrices, ABA = A?