MathDB
IMC 2009 Day 1 P2

Source:

July 15, 2014
IMCcollege contests

Problem Statement

Let A,B,CA,B,C be real square matrices of the same order, and suppose AA is invertible. Prove that (AB)C=BA1    C(AB)=A1B (A-B)C=BA^{-1}\implies C(A-B)=A^{-1}B