This paper deals with the relationships between the concepts of linear dependence and independence of vectors, and the bideterminant of a matrix including the links between the bideterminant and rank of a square matrix in semilinear spaces of $$n$$ n -dimensional vectors over commutative zerosumfree semirings. First, it discusses some properties of bideterminant of a matrix, then introduces the concepts of semi-linear dependence and strong linear independence of a set of vectors, respectively, and gives a necessary and sufficient condition that the bideterminant of a matrix is equal to $$0$$ 0 . In the end, it shows a necessary and sufficient condition that the rank of an $$n$$ n -square matrix is equal to $$n$$ n .