If A = [a_ij<

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

⇒ a_ij = - a_ji …(i)

[for all values of i, j]

For diagonal elements,

⇒ a_ii = - a_ii [for all values of i]

⇒ a_ii + a_ii = 0

⇒ 2a_ii = 0

⇒ a_ii = 0 …(ii)

Now,

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

[from (i) and (ii)]

= 0

Thus,

Hence Proved.