So Gauss-Jordan elimination can be performed through the form of $(A|I)$ where $I$ is the identity matrix. We carry out row elementary operations as usual until the matrix becomes the form $(I|B)$, then the matrix $B$ is the inverse of $A$.
My question is, if I apply Gauss-Jordan elimination without taking into account the structure of the identity matrix in the initial form $(A|I)$ of the augmented matrix, then the computation of A$^{-1}$ requires $3n^3 − 2n^2$ arithmetic operations. I do not understand how this numbers come into meaning. The book says that it is an easy derivation from the operation count $n^3+n^2-n$ of Gauss-Jordan elimination.
Thanks for any input