jee-advanced 2024 Q10

jee-advanced · India · paper1 4 marks Matrices Determinant and Rank Computation
Let $S = \left\{ A = \left( \begin{array} { l l l } 0 & 1 & c \\ 1 & a & d \\ 1 & b & e \end{array} \right) : a , b , c , d , e \in \{ 0,1 \} \right.$ and $\left. | A | \in \{ - 1,1 \} \right\}$, where $| A |$ denotes the determinant of $A$. Then the number of elements in $S$ is $\_\_\_\_$ .
Let $S = \left\{ A = \left( \begin{array} { l l l } 0 & 1 & c \\ 1 & a & d \\ 1 & b & e \end{array} \right) : a , b , c , d , e \in \{ 0,1 \} \right.$ and $\left. | A | \in \{ - 1,1 \} \right\}$, where $| A |$ denotes the determinant of $A$. Then the number of elements in $S$ is $\_\_\_\_$ .