Let $C\in M_n(\mathbb{R})$ and let $D$ be the matrix that results when the rows of $C$ are written in reverse order. What is the relationship between $\det(C)$ and $\det(D)$?
What I tried: I was considering writing $D$ as $C $with row $i$ replaced by 1 times row $(n-i)$ added to row i $\forall i \in \mathbb{N}, i\leq n$ and then finding the determinant of the new $D$ and subtracting $\det(C)$, which would then equal $1+\det(C)$ I believe, but I think that this may be incorrect.
Hint: Let $J$ be the $n$-by-$n$ matrix with $J_{1\leq i,j\leq n}=\delta_{i+j,n+1}$ (i.e. $J_{ij}=1$ along the antidiagonal and zero otherwise). What is the matrix $JC$, and what does this tell you about $\det{D}$?