If `n(A)=n(B)=3`, then how many bijective functions from A to B can be formed?

Answer

To find the number of bijective functions from set A to set B when both sets have the same number of elements, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the cardinality of sets A and B**:
Given that \( n(A) = n(B) = 3 \), we know both sets have 3 elements.

2. **Understand the concept of bijective functions**:
A bijective function is a one-to-one correspondence between the elements of set A and set B. This means every element in A is paired with a unique element in B, and vice versa.

3. **Use the formula for the number of bijective functions**:
The number of bijective functions from a set with \( n \) elements to another set with \( n \) elements is given by \( n! \) (n factorial).

4. **Calculate \( n! \) for \( n = 3 \)**:
Here, since \( n = 3 \), we calculate \( 3! \):
\[ 3! = 3 \times 2 \times 1 = 6 \]

5. **Conclusion**:
Therefore, the total number of bijective functions from set A to set B is 6.

### Final Answer:
The number of bijective functions from A to B is **6**.