SIMON-MARAIS 2021 A3

Let $\mathcal{M}$ be the set of all $2021 \times 2021$ matrices with at most two entries in each row equal to $1$ and all other entries equal to $0$ . Determine the size of the set $\{ \det A : A \in M \}$ . Here $\det A$ denotes the determinant of the matrix $A$ .