hello
please hellp me to prove that the only commutive matrices with aother matrices are the diagonal ???
That is not true. You should change diagonal by scalar. Try now.
Fernando Revilla
Can you be more precise about what you are trying to prove?
It is true that the only matrices that commute with all diagonal matrices are themselves diagonal matrices.
But it is not true that the the only sets of commuting matrices are diagonal. For example, the matrices $\displaystyle \begin{bmatrix}1&x\\0&1\end{bmatrix}$ all commute with each other.
I understood the problem in the same way, but the result is false. Choose:
$\displaystyle D=\begin{bmatrix}{1}&{0}\\{0}&{0}\end{bmatrix},\qu ad A=\begin{bmatrix}{0}&{1}\\{0}&{0}\end{bmatrix}$
$\displaystyle D$ is diagonal and however $\displaystyle AD\neq DA$
In Drexel28's web there is a proof that a matrix $\displaystyle M\in\mathbb{K}^{n\times n}$ conmutes with all matrices $\displaystyle A\in \mathbb{K}^{n\times n}$ iff $\displaystyle M$ is an scalar matrix.
Fernando Revilla