Proving the Even Rank of Skew Symmetric Matrices: Induction and Other Methods

bernoli123
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how can we prove that the rank of skew symmetric matrix is even
i could prove it by induction
is there another way
 
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what about thinking of rank-nullity theory
since the dimension of this skew-symmetric matrix=n(n-1)/2
but how to calculate the dim of the AX=0
 

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