If A is a square matrix of order 3 and `|adjA|=25`, then `|A|=`

Options

A. `25`
B. `-25`
C. `pm5`
D. `625`

Answer

To solve the problem, we will use the properties of determinants, specifically the relationship between the determinant of a matrix and the determinant of its adjoint.

### Step-by-Step Solution:

1. **Understand the Given Information**:
We are given that \( A \) is a square matrix of order 3 and \( |adj A| = 25 \).

2. **Use the Property of the Determinant of the Adjoint**:
The property states that for any square matrix \( A \) of order \( n \):
\[ |adj A| = |A|^{n-1} \]
Here, since \( A \) is of order 3, we have:
\[ |adj A| = |A|^{3-1} = |A|^2 \]

3. **Set Up the Equation**:
From the information given, we can set up the equation:
\[ |A|^2 = 25 \]

4. **Solve for \( |A| \)**:
To find \( |A| \), we take the square root of both sides:
\[ |A| = \sqrt{25} \]
This gives us:
\[ |A| = 5 \quad \text{or} \quad |A| = -5 \]

5. **Conclusion**:
Therefore, the determinant of matrix \( A \) can be either \( 5 \) or \( -5 \).

### Final Answer:
\[ |A| = \pm 5 \]