If $A=\left\{\left(\begin{array}{ll}a & b \\ c & d\end{array}\right): a, b, c, d \in\{-1,1\}\right\}$, ,…
If $A=\left\{\left(\begin{array}{ll}a & b \\ c & d\end{array}\right): a, b, c, d \in\{-1,1\}\right\}$, , then the number of singular matrices in $\mathrm{A}$ is
$9$
$12$
$10$
$8$
Solution
Given $S=\left\{\left(\begin{array}{ll}a & b \\ c & d\end{array}\right): a, b, c, d \in\{-1,1\}\right\}$
For singular $a d-b c=0$
$\Rightarrow a d=b c$
So number of singular matrices $=2 \times 2+2 \times 2=8$