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Question
Show that all the diagonal elements of a skew symmetric matrix are zero.
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Solution
Let `A = [a_(ij)]` be a skew−symmetric matrix.
So,
`a_(ij) = -a_(ji)` for all i , j
`=> a_(ii) = -a_(ii)` for all value of i
`=> 2a_(ii) = 0 => a_(ii) = 0` for all value of i
`=> a_(11) = a_(22) = a_(33) = ... = a_"nn" = 0`
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