GATE 2020 CH – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

A $4\times4$ matrix $M=[m_{ij}]$ has all diagonal entries zero and satisfies $m_{ij}=-m_{ji}$. What is the minimum number of elements needed to specify it?

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Correct answer: (B) 6

Explanation

The matrix is skew-symmetric. Its diagonal entries are already fixed to zero, and each entry below the diagonal is the negative of the matching entry above it. Only the upper triangular off-diagonal entries are independent: $4(4-1)/2=6$. Thus B.

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