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