# If A is a symmetr

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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