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Let A=[[2,0,7] , [0,1,0], [1,-2,1]] and ...

Let `A=[[2,0,7] , [0,1,0], [1,-2,1]]` and `B=[[-x,14x,7x] , [0,1,0] , [x,-4x,-2x]]` are two matrices such that `AB=(AB)^(-1)` and `AB!=I` then `Tr((AB)+(AB)^2+(AB)^3+(AB)^4+(AB)^5+(AB)^6)=`

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Verified by Experts

The correct Answer is:
`1//5`
We have
`AB=[(5x,0,0),(0,1,0),(0,10x-2,5x)]=[(1,0,0),(0,1,0),(0,0,1)]`
`implies x=1//5`
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