Let A, B be \(3\times 3\) integer matrices such that A, A+B, A+2B, A+3B, A-B, A-2B, A-3B are invertible and their inverse matrices are all integer matrices. 

Prove that A+4B also has an inverse, and its inverse is again an integer matrix.

The best solution was submitted by Haewon Yoon (윤혜원), 수리과학과 2004학번. Congratulations! 

Here is his Solution of Problem 2008-3.