MathDB

Say that an

n

-by-

n

matrix

A=(a_{ij})_{1\le i,j \le n}

with integer entries is very odd if, for every nonempty subset

S

\{1,2,\dots,n \}

, the

|S|

-by-

|S|

submatrix

(a_{ij})_{i,j \in S}

has odd determinant. Prove that if

A

is very odd, then

A^k

is very odd for every

k \ge 1

B5