Final answer:
Cohesin is the protein that binds sister chromatids along their entire length, ensuring they stay together until anaphase during cell division. Hence, the correct answer is A.
Step-by-step explanation:
The substance that binds sister chromatids along their length is known as cohesin. During cell division, specifically throughout phases like prophase and metaphase, cohesin proteins hold sister chromatids together until they are ready to separate in anaphase.
In contrast, the centromere is a specific region of a chromosome where sister chromatids are most closely joined, but it does not bind them along their entire length. The kinetochore is a protein structure on the chromosome where the spindle fibers attach during cell division, but it also does not serve as a binder for the chromatids' length.