Show all $n\times n$ matrices which $AB=BA$ have a common eigenvector
85581
Matrices commute if and only if they share a common basis of eigenvectors?
130498
Linear algebra proof regarding matrices
114250
If $V_0$ is the subspace of matrices of the form $C=AB-BA$ for some $A,B$ in a vector space $V$ then $V_0=\{A\in V|\operatorname{Trace} (A)=0\}$
19132
Similar matrices have the same eigenvalues with the same geometric multiplicity
31326
Number of $(0,1)$ $m\times n$ matrices with no empty rows or columns
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
35013
Demonstration: If all vectors of $V$ are eigenvectors of $T$, then there is one $\lambda$ such that $T(v) = \lambda v$ for all $v \in V$.
8356
Any $n \times n$ matrix $A$ can be written as $A = B + C$ with $B$ is symmetric and $C$ skew-symmetric.
48658
Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
120867
How prove this two symmetric matrices $AB=0$
36613
Prove that simultaneously diagonalizable matrices commute
5616
How can I prove the IFF condition for this group of matrices?
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
106986
Eigenvalues of $AB$ and $BA$
133036
Jordan normal form and invertible matrix of generalized eigenvectors proof