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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
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The correct answer is:
$8$
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 $=2 \times 2+2 \times 2=8$
For singular $a d-b c=0$
$\Rightarrow a d=b c$
So number of singular matrices $=2 \times 2+2 \times 2=8$
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