The raising and lowering operators are denoted as L₊ and L_-, respectively. The correct commutator relation between angular momentum (L) and its various components (L_x , L_y and L_z) is

Correct option is D

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In quantum mechanics, the raising (L₊) and lowering (L_-) operators change the magnetic quantum number m, but they do not affect the total angular momentum L²​​. The raising operator L₊ increases the magnetic quantum number m by 1, and the lowering operator L- decreases it by 1.
The commutator between the total angular momentum L² and these raising and lowering operators is zero because applying these operators does not change the total angular momentum magnitude L².
The total angular momentum operator L² represents the magnitude of the angular momentum vector, while the raising and lowering operators only affect the projection along the z-axis (i.e., L_z).
The commutator of L²with the raising and lowering operators is zero because they do not affect the magnitude of the total angular momentum. Instead, they modify only the L_z component.