$AB-BA=A$, Then A is singular?
13346
If $A=AB-BA$, is $A$ nilpotent?
84626
Why in these matrices are $AB=BA$ not equal? What is the logic behind them?
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$
18297
Suppose that each of the row sums of an $n\times n$ matrix $A$ is equal to zero. Show that $A$ must be singular.
78755
If matrix $A$ is unitary and $B^2=A$, is $B$ necessarily unitary?
6267
Matrices: system that is "computationally singular" versus "exactly singular"
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
89190
Why is it true that $|AB:A|=|B:A\cap B|$ even if $A$ is not normal in $AB$? (Second Isomorphism Theorem)
129007
Relation between AB and BA
78736
Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
59397
Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
89177
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
140290
Solving $AB - BA = C$
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?
110502
$AB=BA$ with same eigenvector matrix
74460
Matrices A+B=AB implies A commutes with B
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$