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Why is this anti-symmetrical and symmetrical at the same time? I get how it is anti-symmetric because There is no pair such as (1,2) & (2,1) but how did it become symmetrical?

R is a relation on the set of integers R = {(a,b) | a = b} 
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    You may wish to chec$k$ your definition of symmetric. You may have misunderstood it.2012-10-07

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If $(a,b)$ is in $R$ then $a=b$ [by the definition given for $R$] so $(b,a)=(a,b)$ so $(b,a)$ is in $R$.