Which of the following is correct ?

Options

A. Determinant is a square matrix
B. Determinant is a number associated to a matrix
C. Determinant is a number associated to a square matrix
D. None of these

Answer

To solve the question, we need to analyze the given statements about determinants and determine which one is correct.

### Step-by-Step Solution:

1. **Understanding the Definition of a Determinant**:
- A determinant is a scalar value that can be computed from the elements of a square matrix. It provides important information about the matrix, such as whether it is invertible.

**Hint**: Remember that determinants are associated only with square matrices.

2. **Analyzing Statement 1**: "Determinant is a square matrix."
- This statement is incorrect. A determinant is not a matrix; it is a number (scalar) that is derived from a square matrix.

**Hint**: Think about what a determinant represents and whether it can be a matrix itself.

3. **Analyzing Statement 2**: "Determinant is a number associated with a matrix."
- This statement is partially correct but misleading. While it states that a determinant is a number associated with a matrix, it does not specify that this is only true for square matrices. Determinants can only be calculated for square matrices.

**Hint**: Consider the types of matrices for which determinants can be calculated.

4. **Analyzing Statement 3**: "Determinant is a number associated to a square matrix."
- This statement is correct. The determinant is indeed a scalar value that is computed from the elements of a square matrix.

**Hint**: Recall the process of calculating the determinant for a square matrix, such as a 2x2 or 3x3 matrix.

5. **Conclusion**:
- Based on the analysis, we find that Statement 3 is the correct option. Statements 1 and 2 are incorrect.

### Final Answer:
The correct statement is: **"Determinant is a number associated to a square matrix."**