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KCET2023MathematicsMatrices

If A and B are two matrices, such that A B=B and B A=A , then A^2+B^2 equals to

Options

  1. A2 A B
  2. BA B
  3. C2 B A
  4. DA+B

Correct answer

D. A+B

Step-by-step solution

Given, A B=B and B A=AA^2+B^2=A A+B B=A(B A)+B(A B)=(A B)(A)+(B A) B=B A+A B=A+B

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