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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'

PRADEEP 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. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

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  5. Evaluate |[1,x,y],[1,x+y,y],[1,x,x+y]|

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  6. Using properties of determinants, prove that: |[alpha,alpha^2,beta+gam...

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  7. Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1...

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  8. Solve by matrix method 2/x + 3/y + 10/z = 4 , 4/x - 6/y + 5/z = 1 , ...

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  9. If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a],[x+3,x+4,...

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  10. Let A = [[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]], wher...

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  11. Fill in the blanks : If A = [(1,a,3),(2,b,6),(3,c,9)], then det A is...

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  12. Fill in the blanks : If cos 2 theta = 0, then |(0, costheta, sinthet...

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  13. Fill in the blanks : Determinant of a skew symmetric matrix of order...

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  14. Select the Correct Option If A is an invertible matrix of order 2, the...

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  15. Fill in the blanks : If A is an invertible square matrix, then (A)^-...

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  16. If A is matrix of order 3xx3, then (A^(2))^(-1)=…….

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  17. Fill in the blanks : The determinant of a diagonal matrix is equal t...

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  18. The sum of the products of elements of any row with the co-factors of ...

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  19. If A is matrix of order 3xx3, then |3A|=……….

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  20. Fill in the blanks : If A is a square matrix of order n then det (ad...

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