How to prove "A matrix commutating with all Idempotent matrices is necessarly scalar"
49977
Show that the collection of matrices which commute with every idempotent matrix are the scalar matrices
72326
Determinant of block matrix with commuting blocks
49439
Matrix exponential via Cayley-Hamilton Theorem
67990
Commutativity of matrix and its transpose
32487
Proving $\det \left( \begin{smallmatrix} A & -B \\ B & A \end{smallmatrix} \right) =|\det(A+iB)|^2$
154640
Do Diagonal Matrices Always Commute?
35080
If matrices $A$ and $B$ commute, $A$ with distinct eigenvalues, then $B$ is a polynomial in $A$
82020
basic linear algebra question, proving it is a diagonal matrix and scalar matrix.
80544
Need verification - Prove a Hermitian matrix $(\textbf{A}^\ast = \textbf{A})$ has only real eigenvalues
57731
Can commuting matrices $X,Y$ always be written as polynomials of some matrix $A$?
10014
Is there a built-in procedure for simultaneous diagonalization of a set of commuting matrices?
6659
Approximating commuting matrices by commuting diagonalizable matrices
156878
If every commutator is idempotent, then the ring is commutative
2271
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
108742
Proving commutativity of addition for vector spaces
18585
Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
130268
How to prove that a nilpotent matrix is not invertible?