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arXiv · 1709.03382

A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse

Pietro Paparella
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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.

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BibTeXRIS

Pietro Paparella. 2017-09-05. A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse. https://doi.org/10.4169/college.math.j.48.5.366

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