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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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CENGAGE-MATRICES-Exercise 13.5
  1. By the method of matrix inversion, solve the system. [(1,1,1),(2,5,7...

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  2. Let A=[[2,0,7] , [0,1,0], [1,-2,1]] and B=[[-x,14x,7x] , [0,1,0] , [x,...

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  3. Find A^(-1) if A=|(0,1,1),(1,0,1),(1,1,0)| and show that A^(-1)=(A^(2)...

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  4. For the matrix A=[3 1 7 5] , find x and y so that A^2+x I=y Adot

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  5. If A^(3)=O, then prove that (I-A)^(-1) =I+A+A^(2).

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  6. If A=[[cos alpha, -sin alpha] , [sin alpha, cos alpha]], B=[[cos2beta,...

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  7. If A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1,1),(2,2,1),(1,1,1)], D=[(10),...

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  8. If A is a 2xx2 matrix such that A^(2)-4A+3I=O, then prove that (A+3I)^...

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  9. For two unimobular complex numbers z(1) and z(2), find [(bar(z)(1),-z(...

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  10. Prove that inverse of a skew-symmetric matrix (if it exists) is skew-s...

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  11. If square matrix a is orthogonal, then prove that its inverse is also ...

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  12. If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is...

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  13. Prove that ("adj. "A)^(-1)=("adj. "A^(-1)).

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  14. Using elementary transformation, find the inverse of the matrix A=[(a,...

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  15. Show that the two matrices A, P^(-1) AP have the same characteristic r...

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  16. Show that the characteristics roots of an idempotent matris are either...

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  17. If alpha is a characteristic root of a nonsin-gular matrix, then prove...

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