If A = [aij] is a skew-symmetric matrix, then write the value of .
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.