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COMEDK2014MathematicsMatrices

A and B are two matrices such that A B=B , B A=A , then A²+B²=

Options

  1. A2 A B
  2. B2 B A
  3. CA+B
  4. DA B

Correct answer

C. A+B

Step-by-step solution

Given, A B=B Multiply by A on both sides A B A=B A ...(i) Also, B A=A Multiply by B on both sides B A B=A B ...(ii) Adding Eqs. (i) and (ii), we get A B A+B A B=B A+A B A(B A)+B(A B)=B A+A B A A+B B=A+B A²+B²=A+B

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