Q58 / 160 · AP EAMCET 2023 (15 May Shift 2) · Mathematics

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
    $10$
  • Correct answer
    D
    $8$

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 $=2 \times 2+2 \times 2=8$

Hence, the correct answer is option: 'D'.

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