Question

Consider the following statements:

1. Determinant is a square matrix.

2. Determinant is a number associated with a square matrix.

Which of the above statements is/are correct?

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
5. Either 1 nor 2

Answer 1

Correct Answer - Option 2 : 2 only

Concept:

Determinant of a matrix:

For an \(\rm n\times n\) matrix \(A = \left[a_{ij}\right]\) the determinant of A is defined as to be a scaler

\(\rm det(A) = \displaystyle\sum_{p}\sigma(p)a_{1_{p_1}}a_{2_{p_2}}\dots a_{n_{p_n}}\)

where the sum is taken over n! permutations p = (\(\rm p_1, p_2,\dots, p_n\)) of (1, 2, 3, ... , n).

 

Calculation:

Observe that any matrix is a vector but determinant is a scaler. Therefore, determinant is not a square matrix.

For any square matrix A the determinant is a scaler associated with that matrix.

That means it is a number associated with a square matrix.