Angular momentum — UPSC Physics Optional IFoS 2022 Paper II

The components of the angular momenta \vec{J}_1 and \vec{J}_2 satisfy commutation rules. Show that the components of the sum \vec{J} = \vec{J}_1 + \vec{J}_2 also satisfy the commutation rules. Whether the difference \vec{J}_1 - \vec{J}_2 satisfies an angular momentum?