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Question
If A = [aij] is a skew-symmetric matrix of order n, then ______.
Options
`a_(ij) = 1/(a_(ji)) ∀ i, j`
`a_(ij) ≠ 0 ∀ i, j`
`a_(ij) = 0, where i = j`
`a_(ij) ≠ 0 where i = j`
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Solution
If A = [aij] is a skew-symmetric matrix of order n, then `underline(bb(a_(ij) = 0, where i = j))`.
Explanation:
In a skew-symmetric matrix, the (i, j)th element is negative of the (j, i)th element. Hence, the (i, i)th element = 0
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