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KCET2022MathematicsMatrices

If A is a matrix of order 3 3 , then (A^2 )⁻¹ is equal to

Options

  1. A(-A^2 )^2
  2. B(A⁻¹ )^2
  3. CA^2
  4. DNone of these

Correct answer

B. (A⁻¹ )^2

Step-by-step solution

(A^2 )⁻¹=(A)⁻²= (A⁻¹ )^2= (-A⁻¹ )^2=(-A)⁻² (A^2 )⁻¹ A^2, (-A^2 )^2

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