Center of the general linear group is diagonal matrix proof

[jessicaw]

Homework Statement

center of the general linear group is diagonial matrix proof

Homework Equations

The Attempt at a Solution

i write out a n by n matrix and multiply left by a and right by a^-1 and show that it is the same.
I think it can force the matrix to be diagonal but i find it does not work.

Thanks all!

 

[arkajad]

It may be simpler to look at the equation (supposing B is in the center)

BA=AB for all A in GL(n)

and since for all A, then i particular for a bunch of specially invented very simple matrices A.