Question

Let S=\left\\{\begin{pmatrix} 0 & 1 & c \\\ 1 & a & d\\\ 1 & b & e \end{pmatrix}:a,b,c,d,e\in\left\\{0,1\right\\}\ \text{and} |A|\in \left\\{-1,1\right\\}\right\\}, where |A| denotes the determinant of A. Then the number of elements in S is _______.

Answer 1

The correct answer is:16.