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If `A` is square matrix of order `2xx2` such that `A^(2)=I,B=[{:(1,sqrt(2)),(0,1):}]` and `C=ABA` thenA. `C^(2009)=A[{:(1,2009sqrt(2)),(0,1):}]`B. `C^(2009)=A[{:(1,2009+sqrt(2)),(0,1):}]`C. `|C|^(2009)=1`D. `C^(2009)=A[{:(1,2009sqrt(2)),(0,1):}]` |
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Answer» Correct Answer - C::D `(ABA)^(2)=(ABA)(ABA)=AB(AA)BA=AB^(2)A` continuing in the manner `C^(2008)=AB^(2009)A` `B^(2)=[{:(1,2sqrt(2)),(0,1):}],B^(3)=[{:(1,3sqrt(2)),(0,1):}]` Continuing in this manner `B^(2009)=[{:(1,2009sqrt(2)),(0,1):}]` |
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