If A is a skew-symmetric matrix of order 3, then |A|=

Options

A. 0
B. 1
C. 3
D. Data insufficient

Answer

To solve the problem, we need to find the determinant of a skew-symmetric matrix \( A \) of order 3.

### Step-by-Step Solution:

1. **Understanding Skew-Symmetric Matrices**:
A matrix \( A \) is called skew-symmetric if \( A^T = -A \). This means that the transpose of the matrix is equal to the negative of the matrix itself.

**Hint**: Recall the definition of skew-symmetric matrices.

2. **Properties of Determinants**:
We know that the determinant of a matrix is equal to the determinant of its transpose, i.e., \( |A| = |A^T| \).

**Hint**: Use the property that \( |A| = |A^T| \).

3. **Applying the Skew-Symmetric Property**:
Since \( A \) is skew-symmetric, we have:
\[ |A^T| = |-A| \]
Using the property of determinants, we know that \( |-A| = (-1)^n |A| \), where \( n \) is the order of the matrix. Here \( n = 3 \).

**Hint**: Remember that \( |-A| = (-1)^n |A| \).

4. **Calculating the Determinant**:
Therefore, we can write:
\[ |A| = |-A| = (-1)^3 |A| = -|A| \]
This simplifies to:
\[ |A| = -|A| \]

5. **Solving the Equation**:
Adding \( |A| \) to both sides gives:
\[ |A| + |A| = 0 \implies 2|A| = 0 \]
Thus, we find:
\[ |A| = 0 \]

6. **Conclusion**:
Therefore, the determinant of the skew-symmetric matrix \( A \) of order 3 is:
\[ |A| = 0 \]

### Final Answer:
\[ |A| = 0 \]