Let $D$ a division ring. Show that $Z(M_n(D)) \simeq Z(D)$ Let $D$ a division ring. Show that $Z(M_n(D)) \simeq Z(D)$.
I'm having trouble mounting the isomorphism, do not know how to proceed.

The main problem is to determine the center of the matrix-algebra. One can show that it is formed by $d I_n$ where $d$ is in the center of $D$. The isomorphism is then rather direct to establish.
(Reposted corrected comment as per OP's proposal.) 
