Hi!
You write X=aI, so i suppose you know that a matrix commutes with any other matrix iff it is a multiple of the identity. The same holds for SL(n,F).
Banach
Goku: What you've written doesn't quite make sense. The center will .
Clearly this set is contained in the center. Conversely, let be in the center. Let be the matrix with 1 in the th position and 0 elsewhere. Then if . Now use the fact that this matrix must commute with .