If $A=\{1,2,3\}$ and $R$ is a relation defined on $A$ such that $R=\{(1,1),(1,2),(2,3),(2,2),(3,3),(3,1)\}$. Then the relation $R$ is:

Reflexive: For $R$ to be reflexive on $A$, $(a,a)\in R$ for all $a\in \{1,2,3\}$.Here $(1,1),(2,2),(3,3)\in R$. So, $R$ is reflexive.Symmetric: For $R$ to be symmetric, $(a,b)\in R⟹(b,a)\in R$.Here $(1,2)\in R$ but $(2,1)\notin R$. Also $(2,3)\in R$ but $(3,2)\notin R$. So, $R$ is not symmetric.Transitive: For $R$ to be transitive, $(a,b)\in R$ and $(b,c)\in R⟹(a,c)\in R$.Here $(1,2)\in R$ and $(2,3)\in R$ but $(1,3)\notin R$. So, $R$ is not transitive.Conclusion: $R$ is reflexive but neither symmetric nor transitive.