**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!