Mathematics - Matrix Question with Solution | TestHub

$\left|\begin{array}{ll}\mathrm{a}& \mathrm{d}\\ \mathrm{b}& \mathrm{c}\end{array}\right|=\mathrm{ad}-\mathrm{bc}\Rightarrow \mathrm{ad}=\mathrm{bc}$
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
$\begin{array}{rl}& \Rightarrow 2\times 9=3\times 6\\ & \left|\begin{array}{ll}9& -\\ -& 2\end{array}\right|\Rightarrow {}^4{\mathrm{C}}_1\times 21\end{array}$
Total $=36$