Answer :

Given: A = [aij] is a skew – symmetric matrix

aij = - aji …(i)


[for all values of i, j]


For diagonal elements,


aii = - aii [for all values of i]


aii + aii = 0


2aii = 0


aii = 0 …(ii)


Now,



= 0 + a12 + a13 + … + (-a12) + 0 + a23 + …+ (-a13)+ (- a23)+ 0 + …


[from (i) and (ii)]


= 0


Thus,



Hence Proved.


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