Let A and B be n×n matrices over the real field R. Prove that if A+B is invertible, then A(A+B)^-1B=B(A+B)^-1A.

The best solution was submitted by SeungKyun Park (박승균), 2008학번. Congratulations!

Here is his Solution of Problem 2009-19.

Alternative solutions were submitted by 옥성민 (수리과학과 2003학번, +3), 노호성 (물리학과 2008학번, +3), 송지용 (수리과학과 2006학번, +3), 김현 (2008학번, +3), 정성구 (수리과학과 2007학번, +3), 이재송 (전산학과 2005학번, +3), 정지수 (수리과학과 2007학번, +3), 김호진 (2009학번, +3), 최석웅 (수리과학과 2006학번, +3), 김환문 (물리학과 2008학번, +3),  류종하 (서울대학교 전기과 2008학번). One incorrect solution was received. Thank you for the participation.