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GATE 2016 ME (ME3) – Question 11

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors · 1 mark · Multiple choice

A real square matrix A is called skew-symmetric if

  1. $A^T=A$
  2. $A^T=A^{-1}$
  3. $A^T=-A$
  4. $A^T=A+A^{-1}$

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Correct answer: (C) $A^T=-A$

Explanation

A real matrix is skew-symmetric when its transpose equals its negative: Aᵀ=−A. This forces every diagonal entry to zero and opposite off-diagonal entries to have opposite signs. Thus **C**. Symmetry instead requires Aᵀ=A.