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Let A be a non-singular square matrix of order 3 `xx`3. Then |adj A| is equal to (a) `|A|` (B) `|A|^2` (C) `|A|^3` (D) `3|A|`

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The correct Answer is:
(b)
`"(adj A).A=|A|."I_(3)=|A|[{:(1,0,0),(0,1,0),(0,0,1):}]`
`=[{:(|A|,0,0),(0,|A|,0),(0,0,|A|):}]`
`rArr" |dj A|.A| ="[{:(|A|,0,0),(0,|A|,0),(0,0,|A|):}]=|A|^(3)`
`rArr" |adj A |=|A|"^(2)`
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NAGEEN PRAKASHAN-DETERMINANTS-Exercise 4.5
  1. Find the adjoint of each of the matrices [{:(1,2),(3,4):}]

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  2. Find the adjoint of each of the matrices [{:(1,-1,2),(2,3,5),(-2,0,1...

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  3. Varify A (adjA)=(adjA)A=|A| I [{:(2,3),(-4,-6):}]

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  4. Varify A (adjA)=(adjA)A [{:(1,-1,2),(3,0,-2),(1,0,3):}]=

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

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

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  7. Find the inverse the matrix (if it exists)given in[1 2 3 0 2 4 0 0 5]

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  8. Find the inverse the matrix (if it exists)given in [1 0 0 3 3 0 5 2-1]

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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 the inverse the matrix (if it exists)given in[1-1 2 0 2-3 3-2 4]

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  11. Find the inverse the matrix (if it exists)given in[0 0 0 0cosalphasina...

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

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  13. If A=[[3,1],[-1,2]], I=[[1,0],[0,1]] and O=[[0,0],[0,0]], show that A...

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  14. Solve system of linear equations, using matrix method, x y" "+" "2...

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  15. For the matrix A=[1 1 1 1 2-3 2 1 3]. Show that A^3-6A^2+5A+11 I=0. He...

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

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

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

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