The magnetic dipole moment is a measure of the strength and orientation of a magnetic source, such as a bar magnet or a current loop. It is defined as the product of the current flowing in a loop and the area of the loop. The formula for the magnetic dipole moment (\( \mu \)) is given by:
\[
\mu = I \times A
\]
Where:
- \( I \) is the current flowing through the loop (measured in Amperes, A),
- \( A \) is the area of the loop (measured in square meters, m\(^2\)).
The magnetic dipole moment is often used to describe the magnetic properties of materials and is directly proportional to the current and the area of the magnetic source.
Since the unit of current is Ampere (A) and the unit of area is square meters (m\(^2\)), the unit of the magnetic dipole moment is A m\(^2\). Therefore, the correct option is (A).