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Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Veri...

Let `A = [[1,-2,1],[-2,3,1],[1,1,5]]` Verify that `(A^-1)^-1 = A`

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Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that [adj A]^-1 = adj (A^-1)

If A = [[2,-1,1],[-1,2,-1],[1,-1,2]] , Verify that A^3-6A^2+9A-4I=O and hence find A^-1 .

Let A = [[3,7],[2,5]] and B = [[6,8],[7,9]] Verify that (AB)^-1 = B^-1A^-1

If A=[(1,2,5),(2,3,1),(-1,1,1)] verify that A^(-1)A="AA"^(-1)=I

If A=[[1,2,2],[2,1,2],[2,2,1]] , verify that : A^2-4A-5I=O

If A = [[-1,2,3],[5,7,9],[-2,1,1]] and B = [[-4,1,-5],[1,2,0],[1,3,1]] , then verify that (A-B)' = A' - B'

If A= [[1,2,2,],[2,1,2,],[2,2,1,]] then verify A^-1A=I

If A = [[2,3],[1,-4]], B = [[1,-2],[-1,3]] ,then verify that (AB)^-1 = B^-1A^-1

If A = [[-1,2,3],[5,7,9],[-2,1,1]] andB = [[-4,1,-5],[1,2,0],[1,3,1]] , then verify that (A+B)' = A' + B'

If A' = [[3,4],[-1,2],[0,1]] and B = [[-1,2,3],[1,2,3]] , then verify that (A - B)' = A' - B'

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. If A^-1 = [[3,-1,1],[-15,6,-5],[5,-2,2]] and B = [[1,2,-2],[-1,3,0],[0...

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  2. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that [adj A]^-1 = adj (A^-1...

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  3. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that (A^-1)^-1 = A

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  4. Find |A|: A = {:[(1,-2,2),(2,3,5),(-2,0,1)]

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  5. Verify A(adj A) = (adj A).A = |A|.I : [[1,-1,2],[3,0,-2],[1,0,3]]

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  6. Find |A|: A = {:[(2,1,5),(3,-2,-4),(-3,1,-2)]

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  7. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)].

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  8. Find the determinant of the matrix : A = {:[(a,b),(c,bc)]

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  9. Find the determinant of the matrix : A = {:[(a,b),(c,(1+bc)/a)]

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  10. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)].

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  11. Find the inverse of the matrix : A = [(costheta,sintheta),(-sintheta,c...

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  12. Find the transpose of the matrix : A = {:[(a,b),(c,(1+bc)/a)]

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  13. Find the inverse of the matrix : {:[(2//13,-5//3),(3//13,-1//13)]

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  14. Find the inverse of the matrix : {:[(3/14,1/7),(-2/7,1/7)]

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  15. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)] and show t...

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  16. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)] and show t...

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  17. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)] and show t...

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  18. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)] and show t...

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  19. By using elementary transformation find the inverse of the matrix : A ...

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  20. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)] and show t...

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