If A is a 3-rowed square matrix and |A|=5 then |adjA|=?

Options

A. 5
B. 25
C. 125
D. none of these

Explanation

To find the value of |adj A| for a 3x3 matrix A where |A| = 5, we can use the property of determinants related to the adjoint of a matrix.

### Step-by-step Solution:

1. **Understand the Given Information**:
- We have a 3x3 matrix A.
- The determinant of A, denoted as |A|, is given to be 5.

2. **Use the Property of Determinants**:
- There is a property that relates the determinant of a matrix and its adjoint. For any n x n matrix A, the determinant of the adjoint of A is given by:
\[ |adj A| = |A|^{n-1} \]
- Here, n is the order of the matrix. Since A is a 3x3 matrix, n = 3.

3. **Calculate n - 1**:
- We calculate n - 1:
\[ n - 1 = 3 - 1 = 2 \]

4. **Substitute the Values**:
- Now we can substitute the value of |A| into the formula:
\[ |adj A| = |A|^{2} = 5^{2} \]

5. **Calculate the Result**:
- Calculate \(5^2\):
\[ 5^2 = 25 \]

6. **Final Answer**:
- Therefore, the determinant of the adjoint of A is:
\[ |adj A| = 25 \]

### Conclusion:
The value of |adj A| is 25.