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Let A=[(3, 7),( 2, 5)]and B=[(6, 8),( 7,...

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

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To verify that \((AB)^{-1} = B^{-1}A^{-1}\) for the matrices \(A\) and \(B\), we will follow these steps: ### Step 1: Define the matrices Let: \[ A = \begin{pmatrix} 3 & 7 \\ 2 & 5 \end{pmatrix}, \quad B = \begin{pmatrix} 6 & 8 \\ 7 & 9 \end{pmatrix} \] ...
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NCERT-DETERMINANTS-EXERCISE 4.5
  1. For the matrix A=[(1, 1, 1),( 1, 2,-3),( 2, 1, 3)]. Show that A^3-6A^2...

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  2. For the matrix A=[[3,2],[1,1]], find the numbers a and b such that A^2...

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  3. If A is an invertible matrix of order 2, then det (A^(-1))is equal to...

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  4. Find the inverse the matrix (if it exists)given in[(1, 0, 0),( 0,cosal...

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

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  6. Let A be a non-singular square matrix of order 3 xx3. Then |adj A| is ...

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  7. If A=[[2,-1, 1],[-1 ,2,-1],[ 1, -1, 2]].Verify that A^3-6A^2+9A-4I=0an...

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  8. Find the inverse the matrix (if it exists)given in[[1, 0, 0],[ 3, 3, 0...

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  9. Find the inverse the matrix (if it exists) given in[(2, 1, 3),( 4,-1, ...

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  10. Find adjoint of the matrice in[(1,-1, 2),( 2, 3, 5),(-2, 0, 1)]

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  11. Verify A (a d j A) = (a d j A) A = |A|I " " " " " where A=[(2 ,3),(-4...

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  12. Find adjoint of the matrice in[(1, 2),( 3, 4)]

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  13. Find the inverse the matrix (if it exists)given in[(-1, 5),(-3, 2)]

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  14. Find the inverse the matrix (if it exists)given in[(1, 2, 3),( 0, 2, 4...

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  15. Verify A (a d j A) = (a d j A) A = |A|I [(1,-1,2),(3,0,-2),(1,0,3)]

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  16. Find the inverse the matrix (if it exists)given in[(2,-2),( 4, 3)]

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  17. Find the inverse the matrix (if it exists)given in[(1,-1, 2),( 0, 2,-3...

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  18. If A=[(3, 1),( 1, 2)], show that A^2-5A+5I=0. Hence, find A^(-1).

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