Let's talk about the concept of inverse matrix. Generally, for a square matrix, AB = E. In this case, AB is the inverse matrix of each other, and BA=E can be deduced, where E is identity matrix (unitary matrix). In addition, there are several kinds of generalized inverses (also called pseudo-inverses), and there are often generalized inverses for non-square matrices. There are many definitions of generalized inverses, such as Moore-Penrose generalized inverses and Drezin generalized inverses, which correspond to different applications, but for invertible matrices, they all become conventional inverses, that is, they are all generalizations of conventional inverses.
Mathematically, a matrix is a set of complex numbers or real numbers arranged in a rectangular array [1], which originates from a square matrix composed of coefficients and constants of an equation. This concept was first put forward by British mathematician Kelly in19th century.