Statement-1 (Assertion and Statement- 2 (Reason)
Each of these questions also has four alternative
choices, only one of which is the correct answer. You
have to select the correct choice as given below.
Statement - 1 If A is skew-symnmetric matrix of order 3,
then its determinant should be zero.
Statement - 2 If A is square matrix,
`det (A) = det (A') = det (-A')`

Options

A. Statement-1 is true, Statement -2 is true, Statement-2
is a correct explanation for Statement-1
B. Statement-1 is true, Statement-2 is true, Sttatement - 2
is not a correct explanation for Stamtement-1
C. Statement 1 is true, Statement - 2 is false
D. Statement-1 is false, Statement-2 is true

Explanation

To solve the problem, we need to analyze both statements provided in the question regarding a skew-symmetric matrix and the properties of determinants.

### Step 1: Analyze Statement 1
**Statement 1**: If \( A \) is a skew-symmetric matrix of order 3, then its determinant should be zero.

1. **Definition of Skew-Symmetric Matrix**: A matrix \( A \) is skew-symmetric if \( A^T = -A \).
2. **Property of Determinants**: We know that \( \text{det}(A) = \text{det}(A^T) \).
3. **Applying the Property**: Since \( A^T = -A \), we have:
\[ \text{det}(A) = \text{det}(-A) \]
4. **Using the Determinant Property**: The determinant of a scalar multiple of a matrix is given by:
\[ \text{det}(kA) = k^n \cdot \text{det}(A) \]
where \( n \) is the order of the matrix. Here, \( k = -1 \) and \( n = 3 \):
\[ \text{det}(-A) = (-1)^3 \cdot \text{det}(A) = -\text{det}(A) \]
5. **Setting up the Equation**: From the above, we have:
\[ \text{det}(A) = -\text{det}(A) \]
This implies:
\[ 2 \cdot \text{det}(A) = 0 \implies \text{det}(A) = 0 \]
6. **Conclusion for Statement 1**: Therefore, Statement 1 is **true**.

### Step 2: Analyze Statement 2
**Statement 2**: If \( A \) is a square matrix, then \( \text{det}(A) = \text{det}(A^T) = \text{det}(-A^T) \).

1. **Property of Determinants**: For any square matrix \( A \), we know:
\[ \text{det}(A) = \text{det}(A^T) \]
This part of the statement is **true**.
2. **Analyzing \( \text{det}(-A^T) \)**: We have:
\[ \text{det}(-A^T) = (-1)^n \cdot \text{det}(A^T) = (-1)^n \cdot \text{det}(A) \]
where \( n \) is the order of the matrix.
3. **For Order 3**: Since \( n = 3 \):
\[ \text{det}(-A^T) = -\text{det}(A) \]
4. **Conclusion for Statement 2**: The statement claims that \( \text{det}(A) = \text{det}(-A^T) \), which is not true because \( \text{det}(-A^T) = -\text{det}(A) \). Therefore, Statement 2 is **false**.

### Final Conclusion
- **Statement 1** is **true**.
- **Statement 2** is **false**.