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JEE Main2015MathematicsMatricesActual

If A = 0 1 - 1 0 , then which one of the following statements is not correct?

Options

  1. AA 3 + I = A A 3 - I
  2. BA 4 - I = A 2 + I
  3. CA 2 + I = A A 2 - I
  4. DA 3 - I = A ( A - I )

Correct answer

C. A 2 + I = A A 2 - I

Step-by-step solution

A   = 0 - 1 1 0 A 2 =   0 - 1 1 0 0 - 1 1 0 =   - 1 0 0 - 1 A 3 = - 1 0 0 - 1 0 - 1 1 0 = 0 1 - 1 0 A 4 = 0 1 - 1 0 0 - 1 1 0 = 1 0 0 1 Option 1 A 3 + I =   A   A 3 - I     0 1   - 1 0     - 1 - 1     1 - 1 =   1 - 1   1 1 1 - 1   1 1 = 1 - 1   1 1 .....Correct Option 2 A 4 - I = A 2 + I 0 0 0 0 =   0 0 0 0 ....Correct Option 3 0 0 0 0 =   0 - 1 1 0 ×   - 2 0 0 - 2   =   0 2 - 2 0 .....Incorrect Option 4 A

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