Is matrix equality $AB-BA=I$ impossible?
7622
$AB-BA=I$ having no solutions
25682
If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
8638
If I know $AB$, how can I calculate $BA$?
54294
Can the product $AB$ be computed using only $+, -,$ and reciprocal operators?
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$
131611
$A^TA$ is always a symmetric matrix?
118061
How to check if a matrix is diagonizable?
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
95227
Is the set of all $n\times n$ matrices, such that for a fixed matrix B  AB=BA, a subspace of the vector space of all $n\times n$ matrices?
42446
Simple Elementary Algebra Equality
6091
Similarity of products $AB$ and $BA$ of square matrices
78298
On the nilpotence of the matrix $AB-BA$
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?
33542
When is $A- B = B- A$?
106986
Eigenvalues of $AB$ and $BA$
125647
Solutions to the matrix equation $\mathbf{AB-BA=I}$ over general fields
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$