By the inverse of a matrix we mean the negative of the multiplicand or the multiplier matrix. One matrix can be inverse of another matrix if the product of these two matrices in both their alternate order results in an identity or unit matrix (i.e. 1). Thus, the matrix A will be the inverse of the matrix B, and vice versa, if AB = 1, and also BA = 1. To put it otherwise, A. A-1 = 1, and B. matrix A or as B-1 = 1. In such cases, the matrix B will be represented as the inverse of the matrix A or as A-1 and the matrix A will be represented as the inverse of the matrix B or B-1.
a) The given matrix must be a non-singular one i.e. its determinant must not be 0.
b) The product of the matrix and its inverse must result in a unit matrix, i.e., A, A-1or B. B-1 = 1.
Methods of Computation
Broadly speaking, there are three important methods of determining the inverse of a matrix.
i. Ad joint or Co factor Method.
ii. Elementary (E) operation or Gauss-Jordan Method
iii. Short-out Method.