If the long lashes were caused by being homozygous recessive then A and her mate would have to be homozygous recessive. If both were homozygous recessive, then all of their offsprings would also have to be homozygous recessive and have long lashes.
However, that is not the case. So the long lashes is caused by the presence of a dominant allele. So even if a person is heterozygous, they would still have the long lashes.
If A and her mate were homozygous dominant, then all of their offsprings would also be homozygous dominant and have long lashes. Since A can neither be homozygous recessive nor homozygous dominant, she has to be heterozygous.
C could either be homozygous dominant or heterozygous.
D and E have to be homozygous recessive since they have short lashes and the only way to have short lashes is to be homozygous recessive.