In our logic class, we are supposed to create incidence matrices representing relations with certain properties. For example:

Display the incidence matrix for a relation that is: Reflexive, not symmetric, antisymmetric, and not transitive.

I know how each of these properties works, but it is very tedious the way I do it (guess and check). I noticed that all reflexive matrices have 1's down the left diagonal. Is there any way to immediately know from looking at an incidence matrix whether it has each property?