No, it is inelastic:
- inelastic means the demand is more or less independet of the price; you can't "just stop renting & living" if prices are going up, your options to bypass are highly limited -> therefore its called >inelastic<
You can "just stop renting" and move somewhere else.
Housing demand is less elastic than, let's say, potato demand, but it's not "absolutely inelastic" as you have said.
Good transit and road infrastructure also both make demand more elastic because the choice of where you can live without changing jobs expands.