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KCET2009MathematicsMatrices

If A and B are square matrices of the same order such that (A+B)(A-B)=A²-B² , then (A B A⁻¹ )² is equal to

Options

  1. AB ²
  2. BI
  3. CA ² ~B ²
  4. DA ²

Correct answer

A. B ²

Step-by-step solution

Given, (A+B)(A-B)=A²-B² A²-A B+B A-B²=A²-B² AB = BA Now, ( ABA ⁻¹ )²= ( BAA ⁻¹ )²= B ²

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