If A is non singular then `|A|= 0`. True or False.

Answer

To determine whether the statement "If A is non-singular then |A| = 0" is true or false, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- A **singular matrix** is defined as a square matrix whose determinant is equal to zero. This means that it does not have an inverse.
- A **non-singular matrix** is a square matrix whose determinant is not equal to zero. This means that it has an inverse.

2. **Analyze the Given Statement**:
- The statement claims that if matrix A is non-singular, then the determinant of A (denoted as |A|) is equal to zero.

3. **Apply the Definitions**:
- Since A is non-singular, by definition, we know that |A| ≠ 0 (the determinant is not zero).
- Therefore, the statement that |A| = 0 contradicts the property of non-singular matrices.

4. **Conclusion**:
- Since the determinant of a non-singular matrix cannot be zero, the statement "If A is non-singular then |A| = 0" is **False**.

### Final Answer:
The statement is **False**.

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