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AP EAMCET20228 Jul 2022Evening ShiftMathematicsMatricesActual

If A and B are n n square matrices such that (2 A+B)^2+(A-3 B)^2=5 A^2-2 A B+10 B^2 , then A B A B=

Options

  1. A1 2 [(A-B)^2+(A+B)^2 ]
  2. B4 A B
  3. C1 2 [(A+B)^2-(A-B)^2 ]
  4. DA^2 B^2

Correct answer

D. A^2 B^2

Step-by-step solution

Given, (2 A+B)^2+(A-3 B)^2=5 A^2-2 A B+10 B^2 4 A^2+B^2+2 A B+2 B A+A^2+9 B^2-3 A B-3 B A-5 A^2+2 A B-10 B^2=0 A B-B A=0 A B=B A Then, A B A B=(A B)(A B)=(A A)(B B)=A^2 B^2

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