If A is square matrix of order 3 and |A| = 7 then the value of |adj A| is a) 47 b) 7 c) 49 d) `7^(3)`

Options

A. 47
B. 7
C. 49
D. `7^(3)`

Answer

To find the value of \(|\text{adj } A|\) given that \(|A| = 7\) and \(A\) is a square matrix of order 3, we can use the property of determinants related to the adjoint of a matrix.

### Step-by-Step Solution:

1. **Understand the relationship between the determinant of a matrix and its adjoint**:
The determinant of the adjoint of a matrix \(A\) of order \(n\) is given by the formula:
\[ |\text{adj } A| = |A|^{n-1} \]
where \(n\) is the order of the matrix.

2. **Identify the order of the matrix**:
In this case, the matrix \(A\) is of order 3, so \(n = 3\).

3. **Substitute the values into the formula**:
We know that \(|A| = 7\). Now we can substitute this value into the formula:
\[ |\text{adj } A| = |A|^{3-1} = |A|^{2} \]
Thus,
\[ |\text{adj } A| = 7^{2} \]

4. **Calculate \(7^{2}\)**:
\[ 7^{2} = 49 \]

5. **Final result**:
Therefore, the value of \(|\text{adj } A|\) is \(49\).

### Conclusion:
The answer is \(49\).