What is the number of relations on a set with n elements that are not antisymmetric?

Question

My attempt $A=\{1,2\}$ $$A×A={(1,1),(1,2),(2,1),(2,2)}$$ The total antisymmetric relations on $A×A$ is $12$ And remaining 4 are not antisymmetric. Is it mean if on a particular set if some relations are antisymmetric then the remaining would be not antisymmetric? A set with 3 elements have 216 antisymmetric relations.is it mean the remaining 296 are not antisymmetric? Antisymmetric relations can also be find from $$2^n \times 3 ^{n(n-2)\over 2}$$