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GATE 2022 EE – Question 20

Engineering Mathematics · Linear Algebra: Matrix Algebra · 1 mark · Multiple choice

Consider a $3\times3$ matrix $A$ whose $(i,j)$-th element, $a_{i,j}=(i-j)^3$. Then the matrix $A$ will be

  1. symmetric.
  2. skew-symmetric.
  3. unitary.
  4. null.

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Show answer and explanation

Correct answer: (B) skew-symmetric.

Explanation

$a_{ji}=(j-i)^3=-(i-j)^3=-a_{ij}$ and the diagonal is zero. So $A^T=-A$, which means $A$ is skew-symmetric.