Sometimes educators like to think about test questions as measuring specific things. What are you trying to assess with the question? Depending on what you’re trying to get, you may want to give full credit and some comment about being careful with statements like

$\infty \times \infty \neq \infty$

If you want this to test the knowledge of symbolics and operations with infinity I’d give him zero, although I would feel bad about it.

Sometimes educators like to think about test questions as measuring specific things. What are you trying to assess with the question? Depending on what you’re trying to get, you may want to give full credit and some comment about being careful with statements like

$\infty \times \infty = \infty$

If you want this to test the knowledge of symbolics and operations with infinity I’d give him zero, although I would feel bad about it.