If $A$ and $B$ are $n\times n$ complex matrices , then $AB-BA=I$ is impossible.
7622
$AB-BA=I$ having no solutions
123726
$2\times 2 $ matrices over $\mathbb{C}$ that satisfy $\mathrm A^3=\mathrm A$
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
8356
Any $n \times n$ matrix $A$ can be written as $A = B + C$ with $B$ is symmetric and $C$ skew-symmetric.
136142
Is division of matrices possible?
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
56312
Why can this product of rectangular matrices not be the identity matrix?
146795
Proof If $AB-I$ Invertible then $BA-I$ invertible.
49330
If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?
99585
Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
110502
$AB=BA$ with same eigenvector matrix
55062
$2\times 2$ matrix $C=AB-BA$
43570
Finding two non-zero matrices where $AX = BA$
106322
Let $A$ and $B$ be square matrices of the same size such that $AB = BA$ and $A$ is nilpotent. Show that $AB$ is nilpotent.