RO-NMO 2003 Problem 121

a) Determine the center of the ring of square matrices of a certain dimensions with elements in a given field, and prove that it is isomorphic with the given field.b) Prove that $$\left(\mathcal{M}_n\left( \mathbb{R} \right) ,+, \cdot\right)\not\cong \left(\mathcal{M}_n\left( \mathbb{C} \right) ,+,\cdot\right) ,$$ for any natural number $n\ge 2.$ Marian Andronache, Ion Sava