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

Question

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

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)=`

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - `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`

4 views Answered 2023-02-05 15:29