Is set S is field?

Question

Under the matrix addition and multipliaction ,the set $S= \left\{ \begin{bmatrix} x & y \\ -\overline x & \overline y \end{bmatrix} : x, y \in \mathbb{C}\right\}$ is

Choose the correct option

$1.$ Division ring

$2$ Field

I thinks both option 1) and 2) are correct because all propeties of field are satisfies i have checked its

Is its true ?

Answer 1

That question makes no sense, because $M=\left[\begin{smallmatrix}i&0\\i&0\end{smallmatrix}\right]$ belongs to $S$, but $M^2$ doesn't.