I am confused of some commutative properties of some matrices, so here is the question.
What would constitute(or be the name of) a matrix that is always commutative? Which matrices would satisfy this property?
I am confused of some commutative properties of some matrices, so here is the question.
What would constitute(or be the name of) a matrix that is always commutative? Which matrices would satisfy this property?
Hint: try to prove that such a matrix have the form $\lambda I$ where $\lambda\in\mathbb{F}$ by following these steps:
Show that the matrix can't have a non-zero coordinate that is not on the diagonal
Show that all the coordinate on the diagonal must be the same
To do both steps assume by negation and construct a matrix that does not commute with your matrix to get a contradiction.
The name of all such matrices is scalar matrices
Note: this is an answer for the case of square matrices
Unit matrices $\bf 1$ commute ($[A,B]_-=AB-BA=0$) with all other matrices of the same dimension.