Help with a matrix problem

Question

I'm stuck with the following matrix problem:

Consider $A = $$\{ X \in \mathcal{M}_2(\mathbb{C})\ \mid X = \left( \begin{array}{ccc} a & 0 \\ 0 & b \end{array} \right); a, b \in \mathbb{C}; a, b \neq {0}\}$

Find all sets $H \subset A$ such that $card(H) = 7$ and $X, Y \in H \Leftrightarrow X * Y \in H$