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If A=[(1,0,2),(0,2,1),(2,0,3)], prove th...

If `A=[(1,0,2),(0,2,1),(2,0,3)]`, prove that `A^(3)-6A^(2)+7A+2I=0`.

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The correct Answer is:
`[(0,0,0),(0,0,0),(0,0,0)]=0`
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OMEGA PUBLICATION-MATRICES -MULTIPLE CHOICE QUESTIONS
  1. If A=[(1,0,2),(0,2,1),(2,0,3)], prove that A^(3)-6A^(2)+7A+2I=0.

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  2. Assume X, Y, Z, W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx3 ...

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  3. Assume X, Y, Z, W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx3 ...

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  4. A=[a(ij)](mxxn) is a square matrix, if a. m < n b. m > n c. m ...

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  5. Which of the given values of x and y make the following pair of matric...

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  6. If A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)], then A+A'=1, if the v...

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  7. Matrices A and B will be inverse of each other only if a. AB = BA ...

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  8. If A=[(alpha,beta),(gamma,-alpha)] is such that A^(2)=I, then a. 1 ...

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  9. If the matrix A is both symmetric and skew symmetric, then :

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  10. If A is square matrix such that A^(2)=A, then (I+A)^(3)-7A is equal to...

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  11. If A = [ a(ij)]("mxn") is a rectangular matrix, then

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  12. If A,B symmetric matrices of the same order. Then AB-BA is a a. Ske...

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  13. The number of all possible matrices of order 3xx3 with each entry 0 o...

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  14. If A matrix is symmetric as well as skew symmetric, then a. A is dia...

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  15. Matrices A and B will be inverse of each other only if a. AB = BA ...

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  16. Assume X, Y, Z, W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx3 ...

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  17. Assume X, Y, Z, W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx3 ...

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  18. A=[a(ij)](mxxn) is a square matrix, if a. m < n b. m > n c. m ...

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  19. Which of the given values of x and y make the following pair of matri...

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  20. If A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)], then A+A'=1, if the v...

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  21. Matrices A and B will be inverse of each other only if

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