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KCET2013MathematicsMatrices

If A and B are square matrices of order n such that A²-B²=(A-B)(A+B) , then which of the following will be true?

Options

  1. AEither A or B is zero matrix
  2. BA=B
  3. CA B=B A
  4. DEither A or B is identity matrix

Correct answer

C. A B=B A

Step-by-step solution

Given, aligned A²-B² &=(A-B)(A+B) &=A²-B A+A B-B² aligned aligned & 0 &=-B A+A B & A B &=B A aligned Also, options (a), (b) and (d) satisfy the given condition none of those is a necessary condition for A²-B²=(A-B)(A+B)

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