Q. 275.0( 2 Votes )

If A is a symmetr

Answer :

Given that A is a symmetric matrix

A = AT …(i)


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


(An)T = (A×A×A×A…A)T [for all n Є N]


(An)T = (AT × AT … AT)


[ (AB)T = BTAT]


= A × A … A [from (i)]


= An


(An)T = An


Case 1: If n is an even natural number, then


(An)T = An


So, An is a symmetric matrix


Case 2: If n is odd natural number, then


(An)T = An


So, An is a symmetric matrix


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