A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse
History and Overview
2018-08-15 v1
Abstract
An elementary proof of the two-sidedness of the matrix-inverse is given using only linear independence and the reduced row-echelon form of a matrix. In addition, it is shown that a matrix is invertible if and only if it is row-equivalent to the identity matrix without appealing to elementary matrices. This proof underscores the importance of a basis and provides a proof of the invertible matrix theorem.
Keywords
Cite
@article{arxiv.1709.03382,
title = {A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse},
author = {Pietro Paparella},
journal= {arXiv preprint arXiv:1709.03382},
year = {2018}
}
Comments
To appear as a classroom-capsule in the The College Mathematics Journal