InterviewSolution
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InterviewSolution
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Let `A`, `B` are square matrices of same order satisfying `AB=A` and `BA=B` then `(A^(2010)+B^(2010))^(2011)` equals.A. `A+B`B. `2010(A+B)`C. `2011(A+B)`D. `2^(2011)(A+B)` |
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Answer» Correct Answer - D `(d)` Given `AB=A` and `BA=B` `implies{:(A^(2)=A),(B^(2)=B):}` `implies{:(A^(n)=A),(B^(n)=B):}` `implies(A^(2010)+B^(2010))^(2011)=(A+B)^(2011)` Now `(A+B)^(2)=A^(2)+B^(2)+AB+BA` `=2(A+B)` `implies(A+B)^(k)=2^(k)(A+B)` `implies(A^(2010)+B^(2010))^(2011)=(A+B)^(2011)=2^(2011)(A+B)` |
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