$AB=BA$ and $A$ has $n$ eigenvalues. Prove $B$ is diagonalizable
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
150228
If $E$ has eigenvalues $\lambda_1, \ldots, \lambda_n$, then $B \mapsto [E,B] = EB - BE$ has eigenvalues $\lambda_i - \lambda_j$.
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
149923
eigenvalues of A - aI in terms of eigenvalues of A
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
59397
Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
146795
Proof If $AB-I$ Invertible then $BA-I$ invertible.
116539
Eigenvalues of matrix satisfying $A^2 = A$
84626
Why in these matrices are $AB=BA$ not equal? What is the logic behind them?
106986
Eigenvalues of $AB$ and $BA$
71040
If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?
21758
Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal
135420
Determining eigenvalues, eigenvectors of $A\in \mathbb{R}^{n\times n}(n\geq 2)$.
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$
149629
The Eigenvalues of a block matrix