JEE Advance - Mathematics (2024 - Paper 1 Online - No. 10)
Let $S=\left\{A=\left(\begin{array}{lll}0 & 1 & c \\ 1 & a & d \\ 1 & b & e\end{array}\right): a, b, c, d, e \in\{0,1\}\right.$ and $\left.|A| \in\{-1,1\}\right\}$, where $|A|$ denotes the determinant of $A$. Then the number of elements in $S$ is __________.
Answer
16
Explanation
$$\begin{aligned} & |A|=0(a e-b d)-1(e-d)+c(b-a) \\ & =c(b-a)+(d-e) \end{aligned}$$
$$|\mathrm{A}| \in\{-1,1\}$$ and $$\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e} \in\{0,1\}$$
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