To calculate inverse matrix you need to do the following steps. The system must have the same number of equations as variables, that is, the coefficient matrix of the system must be square. In the MATRIX INVERSE METHOD (unlike Gauss/Jordan), we solve for the matrix variable X by left-multiplying both sides of the above matrix equation (AX=B) by A-1. Inverse of a 2×2 Matrix. Reduce the left matrix to row echelon form using elementary row operations for the whole matrix (including the right one). Multiply the inverse matrix by the solution vector. The result vector is a solution of the matrix equation. About the method. Typically, A-1 is calculated as a separate exercize; otherwise, we must pause here to calculate A-1. To solve a system of linear equations using inverse matrix method you need to do the following steps. About the method. Set the matrix (must be square) and append the identity matrix of the same dimension to it. The conditions for the existence of the inverse of the coefficient matrix are the same as those for using Cramer's rule, that is . In this lesson, we are only going to deal with 2×2 square matrices.I have prepared five (5) worked examples to illustrate the procedure on how to solve or find the inverse matrix using the Formula Method.. Just to provide you with the general idea, two matrices are inverses of each other if their product is the identity matrix. 1. Set the main matrix and calculate its inverse (in case it is not singular).