JEE Advanced 2024 Paper 1Question 1
Let $S=\left\{A=\begin{pmatrix}0&1&c\\1&a&d\\1&b&e\end{pmatrix}: a,b,c,d,e\in\{0,1\}\text{ and }|A|\in\{-1,1\}\right\}$, where $|A|$ denotes the determinant of $A$. Then the number of elements in $S$ is _______.
Determinant
Answer$16$
Solution
Expanding along row 1: $|A|=d-e+c(b-a)$. Enumerating all $32$ choices of $a,b,c,d,e\in\{0,1\}$, $|A|=\pm1$ in exactly $16$ cases.