Q45 / 160 · AP EAMCET 2023 (15 May Shift 2) · Mathematics

If $\operatorname{det}(\mathrm{AB})=(\operatorname{det} \mathrm{A})(\operatorname{det} \mathrm{B})$ and $\mathrm{A}$ is a non-singular matrix of $\operatorname{order} 3 \times 3$, then $\operatorname{det}(\operatorname{adj} A)=$

  • A
    $\operatorname{det}(\mathrm{A})$
  • B
    $(\operatorname{det}(\mathrm{A}))^{-1}$
  • Correct answer
    C
    $(\operatorname{det}(\mathrm{A}))^2$
  • D
    $(\operatorname{det}(\mathrm{A}))^3$

Solution

$\begin{aligned} & \text {Since } \operatorname{adj} A=|A| \Rightarrow|\operatorname{adj} A|=|A|^3 \\ & \Rightarrow|\operatorname{adj} A|=|A|^2\end{aligned}$

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

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