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If M is a square matrix such that M^3=M , then how many values of |M| are possible ?

Options

  1. AOne
  2. BTwo
  3. CThree
  4. DFour

Correct answer

C. Three

Step-by-step solution

Given M^3 = M Taking determinant on both sides, we get: |M^3| = |M| Using the property |A^n| = |A|^n , we have: |M|^3 = |M| |M|^3 - |M| = 0 |M|(|M|^2 - 1) = 0 |M|(|M| - 1)(|M| + 1) = 0 |M| = 0, 1, -1 Thus, there are three possible values for |M| . Answer: Three

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