PrepRung
Sign inSign up free

NDA 2017 Maths · Mathematics · Matrices · medium

The product of two skew-symmetric matrices of the same order is skew-symmetric. 2. The inverse of a non-singular symmetric matrix is symmetric.

Single correct option

Consider the following statements.

1. The product of two skew-symmetric matrices of the same order is skew-symmetric.
2. The inverse of a non-singular symmetric matrix is symmetric.

Which of the statements is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (B) 2 only

For statement 1, (AB)T=BTAT=(−B)(−A)=BA(AB)^T=B^TA^T=(-B)(-A)=BA, which is not −AB-AB in general, so the product need not be skew-symmetric. For statement 2, (A−1)T=(AT)−1=A−1(A^{-1})^T=(A^T)^{-1}=A^{-1}, so it is symmetric. Only statement 2 is correct.
Report a mistake

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake