During linear algebra class, we learnt various facts about square matrices, and most importantly, used the determinant of a given matrix to solve different kinds of problems. However, in real life situation, most of the problems involving matrices cannot be expressed by square matrices. Although there are some methods to reduce the problem by turning those non-square matrices into square matrices, is there a more direct way to study these kinds of non-square matrices? In this talk, I will explain the determinant-like functional for non-square matrices, called determinoid, and study its left multiplicativity.