I have an intuition that at least one of the element should be in the form of diagonal matices with diagonal entries being 1 or -1 (e.g I3)
I don't know if there's any other possiblity
Please give a strong proof
(a similar question is that show the centre of the general linear group GL2(C) consisits of all scalar matrices, I can show all scalar matrices are in the centre, but how to show that they are the only kind?)