Answer
False
Work Step by Step
If $V$ is a vector space then $V$ must satisfies closure property with respect to scalar multiplication ______(1)
In particular, take $x=2\in\mathbf{Z}$ ( Set of integers)
In particular, let $k=\frac{2}{3}\in \mathbf{R} $( Set of real numbers)
Consider $\;\;k.x=2.\frac{2}{3}=\frac{4}{3}$
But $\frac{4}{3}$ is not a integer
So by (1)
Hence, Set of integers $\mathbf{Z}$ is not a vector space.
