Given that A is a square matrix of order 3 and |A|=-4, then |adj A| is equal to:

Options

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

Answer

To find the determinant of the adjoint of a square matrix \( A \) of order 3, we can use the following steps:

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

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

### Step 3: Substitute the values into the formula.
We know that \( |A| = -4 \). Therefore, we can substitute into the formula:
\[ |\text{adj} A| = |A|^{3-1} = |A|^2 \]
This simplifies to:
\[ |\text{adj} A| = |A|^2 = (-4)^2 \]

### Step 4: Calculate the value.
Now we calculate \( (-4)^2 \):
\[ (-4)^2 = 16 \]

### Conclusion:
Thus, the determinant of the adjoint of matrix \( A \) is:
\[ |\text{adj} A| = 16 \]