MathDB
VJIMC 2015 Category II, Problem 1

Source: VJIMC2015

August 10, 2015
Matriceslinear algebracollege contests

Problem Statement

Problem 1 Let AA and BB be two 3×33 \times 3 matrices with real entries. Prove that A−(A−1+(B−1−A)−1)−1=ABA , A-(A^{-1} +(B^{-1}-A)^{-1})^{-1} =ABA\ , provided all the inverses appearing on the left-hand side of the equality exist.
Back to ProblemsView on AoPS