The number of singular matrices of order 2 , whose elements are from the set $\{2,3,6,9\}$ is
Solution
\mathrm{a} & \mathrm{~d} \\ \mathrm{~b} & \mathrm{c}
\end{array}\right|=\mathrm{ad}-\mathrm{bc} \Rightarrow \mathrm{ad}=\mathrm{bc}$
Case-I Exactly 1 no. is used
$\Rightarrow \text { All singular }={ }^4 \mathrm{C}_1$
Case-II Exactly 2 no. is used
$\Rightarrow{ }^4 \mathrm{C}_2 \times 2 \times 2$
Case-III Exactly 3 no. is used
None will be singular
Case-IV Exactly 4 No. is used
ad=bc
$\begin{aligned} & \Rightarrow 2 \times 9=3 \times 6 \\ & \left|\begin{array}{ll}9 & - \\ - & 2\end{array}\right| \Rightarrow{ }^4 \mathrm{C}_1 \times 21\end{aligned}$
Total $=36$
Asked in: JEE Main 2025 (07 Apr Shift 1)