### Matrix Puzzle - Math Puzzle

Source: www.puzzletweeter.com Problem: Let A,B be 2x2 matrices with integer entries. Suppose the matrices A,A+B,A+2B,A+3B,A+4B are all invertible and their inverses are also integer matrices. Then show that A+5B is invertible and it's inverse is an integer matrix. Update (24 June 2014): Solution: Posted by Yashoteja Prabhu (Ex-RA at Microsoft Research, IITB CSE 2011 Alumnus) and Sanchit Gupta in comments!