How is the relation only symmetric?

Question

Question:

If $A= \{a,b,c,d\} $, then the relation $R= \{(a,b),(b,a),(a,a)\} $ is …

The relation should be both Symmetric and transitive, but the answer in my textbook is given to be only Symmetric.

How? It should be transitive as he relation $R$ has elements $(a,b)$ and $(b,a)$ and the as per the definition of transitive relation, the set also contains the element $(a,a)$. How is $R$ not a transitive relation?

Answer 1

$(b,a)$ and $(a,b)$ are in $R$, but $(b,b)$ is not. Hence the relation is not transitive.

Answer 2

It's not transitive because $bRa$ and $aRb$ would imply $bRb$ if it were.