0 votes 0 votes The number of binary matrices of order $N*N$ whose determinant is exactly zero. Linear Algebra linear-algebra + – HeadShot asked Nov 29, 2018 HeadShot 313 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Mk Utkarsh commented Nov 29, 2018 reply Follow Share http://oeis.org/A046747 0 votes 0 votes HeadShot commented Nov 29, 2018 reply Follow Share @Mk Utkarsh yeah i checked that but i didn't find any method or may be i overlooked it. 0 votes 0 votes Mk Utkarsh commented Nov 29, 2018 reply Follow Share let X(n) be number of singular matrices of Number of singular $N \times N$ rational (0,1) matrices. let Y(n) be number of binary matrices of order $N \times N$ whose determinant is exactly zero. $Y(n) =$$\large 2^{(n^2)} - n! * \binom{2^n -1}{n} + n! * X(n)$ I don't think it is required to to remember all these things for GATE. 1 votes 1 votes HeadShot commented Nov 29, 2018 reply Follow Share @Mk Utkarsh actually i thought it also have some trivial method as odd/even #determinant matrices has but someone on SO mentioned it as somehow tough job so yeah may be it wont be asked. 0 votes 0 votes Please log in or register to add a comment.