A nice paper devoted to the matrix extreme points of the operator system \(R\) and their extension properties. It is proved that every pure matrix state on \(R\) extends to a pure matrix state on \(A\), where \(A\) is the unital \(C^\ast\)-algebra containing \(R\). Matrix extreme points of the matrix state space \(S(R)\) are characterized as being pure (i.e. generating extreme rays in the state spaces). These results generalize classical results of Kadison on extensions of extreme states between operator systems and \(C^\ast\)-algebras to the context of matrix convexity. As a consequence, a conceptual proof of an earlier result on decomposing \(C^\ast\)-extreme matrix state into direct sum of pure states is provided.