Question

Which of the following is correct?

• A. Determinant is a square matrix.
• B. Determinant is a number associated to a matrix.
• C. Determinant is a unique number associated to a square matrix.
• D. Determinant is not defined for a square matrix.

Hint:

When answering definition-based questions, look for the option that includes all necessary restrictive conditions. Option (2) is a common trap because it sounds plausible but misses the essential "square" requirement.

Answer 1

The Correct Option is C

To solve the question, we need to understand what a determinant is in the context of matrices.

A determinant is a mathematical property that is calculated from a square matrix. This means that determinants are only defined for square matrices, not rectangular matrices.

Determinants have several useful properties in linear algebra. They can be used to determine if a matrix is invertible, and they are involved in calculating eigenvalues and in solving systems of linear equations, among other applications.

Let's analyze each given option:

1. Option 1: "Determinant is a square matrix." This statement is incorrect because a determinant is not a matrix; it is a scalar value (a number) resulting from a specific calculation applied to a square matrix.
2. Option 2: "Determinant is a number associated to a matrix." This option is partially incorrect because while it is a number, it is specifically associated with a square matrix, not just any matrix.
3. Option 3: "Determinant is a unique number associated to a square matrix." This is the correct option. The determinant of a square matrix is a single, unique number that is calculated using a specific formula involving the elements of the matrix.
4. Option 4: "Determinant is not defined for a square matrix." This is incorrect because determinants are indeed defined for square matrices and are an important mathematical tool in the context of square matrices.

Therefore, the correct answer is that the determinant is a unique number associated to a square matrix.