By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2024 Maths, question 16

Topic: Matrices and determinants

Q16

Consider the following statements in respect of a skew-symmetric matrix AA of order 33 :

  1. All diagonal elements are zero.

  2. The sum of all the diagonal elements of the matrix is zero.

  3. AA is orthogonal matrix.

Which of the statements given above are correct ?

  1. (a) 1 and 2 onlyCorrect answer
  2. (b) 2 and 3 only
  3. (c) 1 and 3 only
  4. (d) 1, 2 and 3

Solution.

Answer: (a) 1 and 2 only

  1. Skew symmetry gives aᵢᵢ=−aᵢᵢ, so every diagonal entry and their sum are zero.
  2. A real skew-symmetric matrix of odd order has determinant zero, whereas an orthogonal matrix has determinant ±1.
  3. Thus statements 1 and 2 are true and 3 is false.