I'm asked to prove the following statement:
Let $A$ be an $n\times n$ matrix ($n\geq 2$) with all its elements being either $+1$ or $-1$. Check that its determinant is an even number (i.e. $det(A)=\pm 2k$, with $k$ being an integer number).
I'm not too sure how should I approach this problem. I don't even know where to start the proof, but a hint or two would be greatly appreciated.
Note: My professor showed how this property holds for several matrices $A$ she wrote down in the blackboard, but never gave a full mathematical demonstration. This is not an exercise or something, it's simply curiosity. I've used all my (very limited) Algebra knowledge to no avail. No demonstrations found on the internet. I asked for some help here, but I think I'll just go and ask her during tutoring hours.