Q. Consider the set $\mathbb A$ of all determinants of order $3$ with entries $0$ or $1$ only. Let $\mathbb B$ be the subset of $\mathbb A$ consisting of all determinants with value $1$ and $\mathbb C$ be the subset of $\mathbb A$ of all the determinants with value $-1$. Choose the correct option:
$(a)$ $\mathbb C$ is empty.
$(b)$ $\mathbb B$ has as many elements as $\mathbb C$
$(c)$ $\mathbb {A=B \cup C}$
$(d)$ $\mathbb B$ has twice as many elements as $\mathbb C$
One way could be to list down all the determinants and count, which is the only thing I could think of. But what if instead of order $3$ we have order $n$?
Also, what is a general way to tackle such problems?