Ring theorem and isomorphic I got a problems as follow

Let $S = \left\{\begin{bmatrix}
a & 0 \\
0 & a \\ \end{bmatrix} | a \in R\right\}$, where $R$ is the set of real numbers. Then $S$ is a ring under matrix addition and multiplication. Prove that  $R$ is isomorphic to $S$.

What is the key to prove it? By definition of ring?But I have no idea how to connect the characteristic of ring to Real number.

Hint: Identify $a$ with \begin{bmatrix} a & 0 \\ 0 & a \\ \end{bmatrix} for each $a$ in $R$. 
