Equivalence Relation Textbook Mistake

Question

I found a question in my textbook but I think the answer provided is wrong. The question says: Let $S$ be a relation defined over $\mathbb R$ such that $(a,b) \in S \iff ab≥0$. Is $S$ equivalence?
Book says that it is.
But let $x=4, y=0$ and $z=-6$ be three real numbers. Then clearly $(x,y),(y,z)\in S$ but $(x,z)\notin S$. Therefore $S$ is intransitive, hence not equivalence relation. Am I doing some conceptual blunder? Please help.