Asked by: Dianne Fisher, by email
No. A shadow is cast because the direct rays of light from a source are blocked by an intervening object. The point on the floor that these rays would otherwise have hit, is consequently less brightly lit than the area around it. It’s not completely dark because there is always some indirect illumination scattered off other surfaces. If you managed to cast a shadow, while invisible, it would mean that you had absorbed or reflected the light rays striking you. And if you’re doing that, then you’re not invisible.
In case you’re still not convinced, imagine standing in the shadow of an invisible person. Do you see the Sun or not? If you can see the Sun, it means there can’t be a shadow. If you can’t, then they aren’t invisible.