I was looking at an old post and want to learn about why the answer is true. I have taken linear algebra but never heard about this. Where can I learn this?
2026-02-22 19:47:31.1771789651
What is the determinant modulo 2?
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Reduce all the entries modulo $2$. That is, odd numbers become $1$, even numbers become $0$. Then work out the determinant. Since that just involves multiplication, addition, and subtraction, the result you get is congruent modulo $2$ to the true answer. In this case, the result was 1, so you know the actual determinant is odd, hence nonzero.