Quantum angular momentum — UPSC Physics Optional IFoS 2018 Paper II

The quantum theory describes the angular momentum (\vec{J}) as a linear operator with three components J_x, J_y and J_z in three dimensions. For the angular momentum operator prove that [J^2, J_i] = 0, where i = x, y, and z and comment on the measurability of J^2 and its components as operators.