AP EAMCET · Maths · Permutation Combination
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
- A \(9\)
- B \(12\)
- C \(10\)
- D \(8\)
Answer & Solution
Correct Answer
(D) \(8\)
Step-by-step Solution
Detailed explanation
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 \(=2 \times 2+2 \times 2=8\)
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