Let AX = B be a system of n smultaneous linear equations with n unknowns.
Statement -1 : If `absA=0and (adjA)B ne 0`, the system is consistent with infinitely many solutions.
Statement -2 : A `(adjA)=absAI`

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, Statement -2 is not a correct explanation for Statement -1.
C. Statement -1 is True, Statement -2 is False.
D. Statement -1 is False, Statement -2 is True.

Explanation

To solve the problem regarding the statements about the system of linear equations represented by \( AX = B \), we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding the Given Statements**:
- **Statement 1**: If \( |A| = 0 \) and \( (\text{adj} A)B \neq 0 \), then the system is consistent with infinitely many solutions.
- **Statement 2**: \( A \cdot (\text{adj} A) = |A|I \).

2. **Analyzing Statement 1**:
- If \( |A| = 0 \), it indicates that the matrix \( A \) is singular, meaning it does not have an inverse.
- For a system of equations to be consistent, it must have at least one solution. However, if \( |A| = 0 \) and \( (\text{adj} A)B \neq 0 \), it implies that the system does not have a solution. Therefore, Statement 1 is **false**.

3. **Analyzing Statement 2**:
- The adjoint of a matrix \( A \), denoted as \( \text{adj} A \), has a property that states \( A \cdot (\text{adj} A) = |A|I \).
- This is a standard result in linear algebra and holds true for any square matrix \( A \).
- Therefore, Statement 2 is **true**.

4. **Conclusion**:
- Since Statement 1 is false and Statement 2 is true, the correct conclusion is that the first statement is incorrect while the second statement is correct.

### Final Answer:
- Statement 1: False
- Statement 2: True