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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Determinants

NDA 2019 · Mathematics · Determinants

Paragraph: Let A and B be (3 × 3) matrices with A=4 and B=3 ....

Paragraph:Let AA and BB be (3×3)(3 \times 3) matrices with det⁡⁡A=4\operatorname\det A=4 and det⁡⁡B=3\operatorname\det B=3.
Question:What is det⁡⁡(2AB)\operatorname\det(2 \mathrm{AB}) equal to ?

Options

  1. A96
  2. B72
  3. C48
  4. D36

Correct answer

A. 96

Step-by-step solution

A and B are (3×3)(3 \times 3) matrices det⁡A=4det⁡B=3∴det⁡(2AB)=(2)3∣A∣∣B∣=23(4)(3)=8(4)(3)=96\begin{aligned} & \operatorname{det} A=4 \\ & \operatorname{det} B=3 \\ & \therefore \operatorname{det}(2 \mathrm{AB})=(2)^3|\mathrm{ A}||\mathrm{B}| \\ & =2^3(4)(3)=8(4)(3)=96\end{aligned}
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