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Manipal MET2012MathematicsMathematical Induction

In the set Q⁺ of all positive rational numbers, the operation * is defined by the formula a * b= a b 6 . Then, the inverse of 9 with respect to * is

Options

  1. A4
  2. B3
  3. C1 9
  4. D1 3

Correct answer

A. 4

Step-by-step solution

Let e be the identity, array lrl & a^* e & =a & a e 6 & =a & e & =6 & a^* a⁻¹ & =e & a^* a⁻¹ & =6 & a a⁻¹ 6 =6 & a⁻¹= 6 6 a & 9⁻¹= 6 6 9 =4 array

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