The classical way to invert a matrix A in a basic linear algebra course augments A by the n ×n identity matrix I and applies the Gauss-Jordan algorithm of Exercise 2 to this augmented matrix (including the solution part, i.e., the division by the pivots .ak k^(n-1)). Then A^-1 shows up where I initially was. How many floating point operations are required for this method? Compare this to the operation count of (8)/(3) n^3+𝒪(n^2) required for the same task using LU decomposition (see Example 5.5

INVERSE TRANSFORMATION MATRIX, BASIC TUTORIAL

Inverse Matrix | Definition, Types & Example