If A is square matrix of order 2xx2 such that A^(2)=I,B=[{:(1,sqrt(2)),(0,1):}] and C=ABA then

If A is square matrix of order 2xx2 such that A^(2)=I,B=[{:(1,sqrt(2))

1.	If A is square matrix of order 2xx2 such that A^(2)=I,B=[{:(1,sqrt(2)),(0,1):}] and C=ABA then
Answer» `C^(2009)=A[{:(1,2009sqrt(2)),(0,1):}]` `C^(2009)=A[{:(1,2009+sqrt(2)),(0,1):}]` `\|C\|^(2009)=1` `C^(2009)=A[{:(1,2009sqrt(2)),(0,1):}]` Solution :`(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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If A is square matrix of order 2xx2 such that A^(2)=I,B=[{:(1,sqrt(2)),(0,1):}] and C=ABA then

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