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If A is an invertible matrix, then de...

If `A` is an invertible matrix, then `det(A^(-1))` is equal to `det(A)` (b) `1/(det(A))` (c) 1 (d) none of these

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

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  2. Find adjoint of the matrice in[1-1 2 2 3 5-2 0 1]

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  3. Verify A (a d j A) = (a d j A) A = |A|I for [(2 ,3),(-4,-6)]

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  4. Verify A" "(a d j" "A)" "=" "(a d j" "A)" "A" "=" "|A|"I" |1-1 2 3 0-...

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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 0-7 2 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)=...

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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\ I3=O ...

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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, then det(A^(-1)) is equal to det(A) (...

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