Given that A is a square matrix of order 2 and |A| = - 4, then ladj Al is equal to:

Options

A. `-4`
B. 4
C. `-16`
D. 16

Answer

To solve the problem, we need to find the determinant of the adjoint of a square matrix \( A \) of order 2, given that \( |A| = -4 \).

### Step-by-step Solution:

1. **Understanding the Determinant of the Adjoint**:
We use the property of determinants that states:
\[ | \text{adj}(A) | = |A|^{n-1} \]
where \( n \) is the order of the matrix \( A \).

2. **Identify the Order of the Matrix**:
Since \( A \) is a square matrix of order 2, we have:
\[ n = 2 \]

3. **Substituting the Values**:
Now, substituting \( n \) into the property:
\[ | \text{adj}(A) | = |A|^{2-1} = |A|^{1} = |A| \]

4. **Using the Given Determinant**:
We know from the problem that \( |A| = -4 \). Therefore:
\[ | \text{adj}(A) | = |A| = -4 \]

5. **Final Result**:
Thus, the determinant of the adjoint of \( A \) is:
\[ | \text{adj}(A) | = -4 \]

### Conclusion:
The answer is \( -4 \).