A be a $3\times 3$ matrix over $\mathbb {R}$ such that $AB =BA$ for all matrices $B$. what can we say about such matrix $A$
4280
A linear operator commuting with all such operators is a scalar multiple of the identity.
22410
Find a symmetric matrix $B$ such that for every $3\times 1$ matrix $\text{x}$
59397
Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
78298
On the nilpotence of the matrix $AB-BA$
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
106986
Eigenvalues of $AB$ and $BA$
18800
If A and B are symmetric is AB=BA true?
125647
Solutions to the matrix equation $\mathbf{AB-BA=I}$ over general fields
84422
$AB=BA$, $AC=CA$ we need to show $BC=CB$
76200
Is the rank of $AB$ always equal to the rank of $BA$?
151443
Find two $2 \times 2$ matrices $A$ and $B$ with the same rank, determinant,...but they are not similar.
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
3330
Square matrices, ABA = A?
85297
find a $3 \times 3$ matrix $A$ such that $A \neq I_3$ and $A^{197}=I_3$.
15416
A weak converse of $AB=BA\implies e^Ae^B=e^Be^A$ from "Topics in Matrix Analysis" for matrices of algebraic numbers.
75117
$\mathrm{rank}(AB-BA)=1$ implies $A$ and $B$ are simultaneously triangularisable
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?