$A$ is said to be elementary if $A$ is isomorphic to some $\mathcal K(\mathscr H)$. A C*-subalgebra $B$ is said to be hereditary if for every $0\leq a\leq b\in B$ we have $a\in B$.
I can see that $A$ is generated by minimal projections which are mutually equivalent, in the sense that if $p,q$ are such minimal projections then there is a $x\in A$ such that $x^*px=q$.
But I do not know what to do next.