MathDB
Invertible Matrices

Source: Romanian District Olympiad 2018 - Grade XI - Problem 1

March 10, 2018
Matriceslinear algebra

Problem Statement

Show that if n≥2n\ge 2 is an integer, then there exist invertible matrices A1,A2,…,An∈M2(R)A_1, A_2, \ldots, A_n \in \mathcal{M}_2(\mathbb{R}) with non-zero entries such that:
A1−1+A2−1+…+An−1=(A1+A2+…+An)−1.A_1^{-1} + A_2^{-1} + \ldots + A_n^{-1} = (A_1 + A_2 + \ldots + A_n)^{-1}.
[hide=Edit.] The 77777th77777^{\text{th}} topic in College Math :coolspeak:
Back to ProblemsView on AoPS