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

[bernoli123]

how can we prove that the rank of skew symmetric matrix is even
i could prove it by induction
is there another way

 

[bernoli123]

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