A Short and Elementary Proof of the Two-Sidedness of the Matrix Inverse. (1st November 2017)

• Record Type: Journal Article
• Authors: Paparella, Pietro
• Is Part Of: College mathematics journal. Volume 48:Number 5(2017)
• Page Start: 366
• Page End: 367
• Publication Date: 2017-11-01
• Subjects: Mathematics -- Study and teaching -- Periodicals; Mathematics -- Periodicals; Mathematics; Mathematics -- Study and teaching; Periodicals; 510.071
• DOI: 10.4169/college.math.j.48.5.366
• Languages: English
• ISSNs: 0746-8342

Abstract

Summary: We give an elementary proof of the two-sidedness of the matrix inverse using only linear independence and the reduced row-echelon form of a matrix, concepts prominent in an elementary linear algebra course. In addition, we show that a matrix is invertible if and only if it is row-equivalent to the identity matrix without appealing to elementary matrices.