Choose the correct answer from the following :
If A is a matrix of order `3xx3" and "|A|=6`, then |adj.A|

Options

A. 36
B. 216
C. 729
D. None of these

Answer

To solve the problem, we need to find the determinant of the adjoint of matrix A, given that the determinant of A is |A| = 6 and A is a 3x3 matrix.

### Step-by-Step Solution:

1. **Understand the properties of determinants**:
The determinant of the adjoint of a matrix A (denoted as adj A) can be expressed using the formula:
\[ | \text{adj} A | = |A|^{n-1} \]
where \( n \) is the order of the matrix A.

2. **Identify the order of the matrix**:
Since A is a 3x3 matrix, we have:
\[ n = 3 \]

3. **Substitute the values into the formula**:
Now, we can substitute the values into the formula:
\[ | \text{adj} A | = |A|^{3-1} = |A|^2 \]

4. **Use the given determinant of A**:
We know that \( |A| = 6 \). Therefore:
\[ | \text{adj} A | = 6^2 \]

5. **Calculate the square of the determinant**:
Now, calculate \( 6^2 \):
\[ | \text{adj} A | = 36 \]

6. **Conclusion**:
Thus, the determinant of the adjoint of matrix A is:
\[ | \text{adj} A | = 36 \]

### Final Answer:
The value of |adj A| is 36.