Q. 224.0( 2 Votes )

# If A = [aij<

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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