### Determinant of Binary Matrix

Source: Introduced to me by Sudeep Kamath (PhD Student, UC at Berkeley, EE IITB Alumnus 2008) Problem: An N by N matrix M has entries in {0,1} such that all the 1's in a row appear consecutively. Show that determinant of M is -1 or 0 or 1. Disclaimer: I could not solve it but I have an awesome solution sent by Pritish Kamath (MSR Research Assistant, CSE IITB Alumnus 2012) Update (2/4/2013): Solution posted by Amol Sahasrabudhe (IITB 2004 Alumnus, Ex-Morgan Stanley Quant Associate, Deutsche Bank Quant Associate) and Piyush Sao (EE IITM Alumnus, Georgia Tech Grad Student) in comments! Thanks a ton. I have posted the solution provided by Pritish Kamath (MSR Research Assistant, CSE IITB Alumnus 2012). All three solutions are essentially the same.