$R =\{( a , b ): a = b \}$

For any element a $\in A,$ we have $(a,\, a) \in R,$ since $a=a$

$\therefore R$ is reflexive.

Now, let $(a, b) \in R$

$\Rightarrow a=b$

$\Rightarrow b=a \Rightarrow(b, a) \in R$

$\therefore R$ is symmetric.

Now, let $(a, b) \in R$ and $(b, c) \in R$

$\Rightarrow a=b$ and $b=c$

$\Rightarrow a=c$

$\Rightarrow(a,\, c) \in R$

$\therefore R$ is transitive.

Hence, $R$ is an equivalence relation.

The elements in $R$ that are related to $1$ will be those elements from set $A$ which are equal to $1$

Hence, the set of elements related to $1$ is $\{1\}$.