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Paragraph: Let A and B be (3 3) matrices with det A=4 and det B=3 . Question: What is det (3 AB ⁻¹ ) equal to ?

Options

  1. A12
  2. B18
  3. C36
  4. D48

Correct answer

C. 36

Step-by-step solution

det (3 AB ⁻¹ )=(3)^3| ~A | | B ⁻¹ |=27 |A| |B| =27 4 3 =36

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