Answer
See below
Work Step by Step
Let take two elements from $S$:
$x=(2,4)$ and $y=(3,9)$
$\Rightarrow x+y=(2,4)+(3,9)=(5,13)$
Since $13 \ne 5^2$
Hence $x+y \notin S$.
$\Rightarrow S$ is not closed under addition.
Set of Rational numbers is closed under usual addition.
Because our scalars can come from set of real numbers
In particular, let $\lambda=2$ be a scalar.
and $(a,b)=(2,4) \in S$
Obtain: $\lambda (a,b)=2.(2,4)=(4,8)$
Since $8 \ne 4^2$
Hence $\lambda A \notin S$
Therefore $S$ is closed under scalar multiplication.