Is it obligatory for a worshipper's eyes to be directed towards the place of prostration, or is it permissible for him to look at other worshippers?

The majority of scholars recommend that the worshipper's gaze should be directed towards the place of prostration. The Malikis, however, state that the gaze should be directed forward. None of these is obligatory. Therefore, you are not obliged to look at the place of prostration, and it is permissible to close your eyes during prayer. This might even be better for you if it leads to greater devotion (khushu') and presence of heart. Some scholars do not consider closing the eyes during prayer to be reprehensible.