Step 1: Understand Assertion (A).
Assertion (A) states that the aggregate of carboxylate ions of fatty acids forms a spherical shape. Soap molecules have a hydrophilic ionic head ($-COO^-$) and a long hydrophobic hydrocarbon tail. In water, these molecules aggregate to minimize unfavorable tail-water contact.
Step 2: Explain the micellar structure.
The aggregates formed are called micelles. The hydrocarbon tails point inward and the ionic carboxylate heads point outward into the aqueous medium. This arrangement naturally forms a spherical structure. Assertion (A) is correct.
Step 3: Understand Reason (R).
Reason (R) states that soap helps in emulsification and washing away of oils. The hydrophobic tails dissolve in oil droplets while the hydrophilic heads remain in water. Oil gets trapped inside the micelle and is washed away. Reason (R) is also correct.
Step 4: Check whether (R) explains (A).
Assertion (A) is about the spherical shape of the aggregate. This shape arises due to the amphiphilic nature of soap and thermodynamic free energy minimization. Reason (R) describes the cleaning action (emulsification), which is a consequence of micelle formation, not its explanation.
Step 5: Conclude the relationship.
Both (A) and (R) are correct. However, (R) does not explain why carboxylate aggregates form a spherical shape. They are both true but independently so.
Step 6: State the final answer.
\[ \boxed{\text{Both (A) and (R) are correct but (R) is not the correct explanation of (A).}} \]