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KCET2010MathematicsMatrices

If A and B are two square matrices of the same order such that A B=B and B A=A , then A ²+ B ² is always equal to

Options

  1. AI
  2. BA + B
  3. C2 AB
  4. D2 BA

Correct answer

B. A + B

Step-by-step solution

array lr Given, AB = B , BA = A & (i) Then, A ²+ B ²= A A + B B & = A ( BA )+ B ( AB ) & [from Eq. (i) ] =( AB ) A +( BA ) B & (by commutative law) = BA + AB & [from Eq. (i)] = A + B & [from Eq. (i) array

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