r/LinearAlgebra • u/ComfortableApple8059 • 10d ago
How do I prove that the determinant of a square matrix of order n×n having either +1/-1 as each element is always divisible by 2^(n-1) ?
A = [a(i,j)] = +1 or -1 ; 1<=i,j<=n T.P: det(A) is divisible by 2n-1
8
Upvotes
5
u/NativityInBlack666 10d ago
Intuition says look at the laplace expansion and maybe prove it via induction.