If $AB = BA$, then $A= λI_n$?
4280
A linear operator commuting with all such operators is a scalar multiple of the identity.
151332
If $A,B$ have eigenvalues $\pm1$, what can I say about the eigenvalues of $AB,BA$?
15416
A weak converse of $AB=BA\implies e^Ae^B=e^Be^A$ from "Topics in Matrix Analysis" for matrices of algebraic numbers.
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
99585
Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?
139317
If $A$ is a complex matrix of size $n$ of finite order then is $A$ diagonalizable ?
145876
$AB-BA=A$ implies $A$ is singular and $A$ is nilpotent.
62850
Linear Algebra: If $A^3 = I$, does $A$ have to be $I$?
98470
If $A \ne \varnothing$, then $\varnothing^A=\varnothing$
87265
If $(A-\lambda{I})$ is $\lambda$-equivalent to $(B-\lambda{I})$ then $A$ is similar to $B$
18800
If A and B are symmetric is AB=BA true?
66709
Are the matrix products $AB$ and $BA$ similar?
53113
$I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
129007
Relation between AB and BA
10828
If $A^2 = I$, then $A$ is diagonalizable, and is $I$ if $1$ is its only eigenvalue