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AP EAMCET202125 Aug 2021Morning ShiftMathematicsFunctionsActual

Let A be the set of all 3 3 scalar matrices with real entries. If f: A R is defined by f(m)= det (m) ; m A , then f is

Options

  1. Aone-one but not onto
  2. Bonto but not one-one
  3. Cbijective
  4. Dneither one-one nor onto

Correct answer

C. bijective

Step-by-step solution

A be a scalar matrix aligned A & = [ array ccc m & 0 & 0 0 & m & 0 0 & 0 & m array ] |A| & =m^3 f(m)=m^3 aligned f(m) is increasing function for all values of m . f(m) is injective. Range of f(m)=R= codomain f(m) is surjective. Hence, f(m) is bijective.

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