Q. 285.0( 1 Vote )

If A is a skew-sy

Answer :

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 an even natural number, then


(An)T = An


[ (-1)2 = 1, (-1)4 =1,… (-1)n = 1]


So, An is a symmetric matrix


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