Q. 295.0( 1 Vote )

# If A is a skew-sy

Let A is a skew – symmetric matrix, then

AT = - A …(i)

Now, we have to check An is symmetric or skew – symmetric

(An)T = (AT)n [for all n Є N]

(An)T = (- A)n [from (i)]

(An)T = (-1)n (A)n

Given that n is odd natural number, then

(An)T = - An

[ (-1)3 = - 1, (-1)5 = - 1,… (-1)n = - 1]

So, An is a skew - symmetric matrix

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