: The correct statement about magnetic moment is :
A. it is vector quantity
B. its unit is \[{\rm{A}}{{\rm{m}}^2}\]
C. its dimensions are \[\left[ {A{L^2}} \right]\]
D. all of the above

Hint: Magnetic moment of a magnet is equal to the product of strength of the pole and distance between the south pole and north pole, the distance between these two poles of the magnet is measured from south to north pole.

Complete step by step answer:
Pole strength is the ability of the magnet to attract the particles towards its respective poles. It is considered as a scalar quantity because it is independent of the direction, but the pole strength of the north pole is considered positive and for the south pole we can consider it as a negative value. From the definition of magnetic moment, we know that it depends on the direction of the distance between the poles of magnet, so we require magnetic as well as direction to define the value of magnetic moment. Therefore, we can say that the magnetic moment is a vector quantity. Therefore, option (A) is correct.
The unit of pole strength is Ampere-metre (Am) and we know that the unit of distance is meter, so the unit of magnetic moment is given the product of pole strength’s unit and distance’ unit, which is given as:
Unit of magnetic moment \[
= {\rm{Am}} \cdot {\rm{m}}\\
= {\rm{A}}{{\rm{m}}^2}
\]
Hence option (B) is also correct.
The dimensional formula for unit of magnetic moment can be written as:
Dimensional formula of magnetic moment \[ = \left[ {A{L^2}} \right]\]
Hence option (C) is also correct.
Therefore, we can say that the magnetic moment is a vector quantity whose unit is \[{\rm{A}}{{\rm{m}}^2}\] and dimension is \[\left[ {A{L^2}} \right]\]. Hence option (D) is correct.

Note: We can note that the unit Ampere itself is the base unit of current, so we cannot convert it further. We have to check all the options, whether they are correct or not, because if we only solve for just one option, then it will lead us to a partially correct answer.