Which of the following statements is correct ?

Options

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

Answer

To determine which statement about determinants is correct, let's analyze each option step by step.

### Step 1: Analyze Option A
**Statement:** Determinant is a number associated to a metric.

- A metric typically refers to a function that defines a distance in a space, such as in metric spaces. Determinants are not associated with metrics but rather with matrices. Therefore, this statement is **incorrect**.

**Hint:** Consider what a metric is and how it relates to matrices and determinants.

### Step 2: Analyze Option B
**Statement:** Determinant is a square matrix.

- A determinant is not a square matrix; rather, it is a scalar value that can be computed from a square matrix. Thus, this statement is also **incorrect**.

**Hint:** Recall the definition of a determinant and the properties of matrices.

### Step 3: Analyze Option C
**Statement:** Determinant is a number associated to a square matrix.

- This statement is accurate. The determinant is a scalar value that can be calculated from a square matrix. It provides important information about the matrix, such as whether it is invertible (a non-zero determinant indicates that the matrix is invertible). Therefore, this statement is **correct**.

**Hint:** Think about the properties and significance of the determinant in linear algebra.

### Step 4: Analyze Option D
**Statement:** None of the above.

- Since we have established that Option C is correct, this statement is **incorrect**.

**Hint:** Evaluate the truth of the previous statements to determine the validity of this option.

### Conclusion
The correct answer is **Option C**: "Determinant is a number associated to a square matrix."