Prove that $\det(A)\neq 0$.
Let $A$ be a $n \times n$ matrix, $n$ even, with even diagonal elements and all other elements odd integers. Prove that $\det(A)\neq 0$. Can anyone give me a hint? Thank you.
Solution 1:
Hint: Compute the determinant of $A$ reduced modulo $2$.
Solution 2:
The determinant is an odd integer then.