GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
180 views

If A3x3 is a matrix with |A| = 2. What is the determinant of Adj (Adj (Adj A))?

asked in Linear Algebra by Active (2k points)   | 180 views

1 Answer

+5 votes
Best answer

We know :

| Adj(A) |  = |A|n-1

Now extending this result we can solve as :

          Adj(A) . Adj(Adj(A))  = |Adj(A)| . I where I is identity matrix

 ==>  | Adj(A) . Adj(Adj(A)) |  =  |Adj(A)|n

 ==>  | Adj(Adj(A)) |          =   |Adj(A)|n-1   = |A|(n-1)^2

 ==> | Adj(Adj(A)) * Adj( Adj(Adj(A)))|    =  | Adj(Adj(A)) |n

 ==> | Adj( Adj(Adj(A))) |      =  | Adj(Adj(A)) |n-1

 ==>  | Adj( Adj(Adj(A))) |     =  | A |(n-1)^3

Now n = 3 here and given |A|  = 2

Therefore 

          | Adj( Adj(Adj(A))) |    = 22^3

==>    | Adj( Adj(Adj(A))) |    = 256

Hence 256 is the correct answer..

answered by Veteran (64.8k points)  
selected by
Top Users Feb 2017
  1. Arjun

    4694 Points

  2. Bikram

    4004 Points

  3. Habibkhan

    3738 Points

  4. Aboveallplayer

    2966 Points

  5. sriv_shubham

    2278 Points

  6. Smriti012

    2212 Points

  7. Arnabi

    1814 Points

  8. Debashish Deka

    1788 Points

  9. sh!va

    1444 Points

  10. mcjoshi

    1444 Points

Monthly Topper: Rs. 500 gift card

20,788 questions
25,938 answers
59,535 comments
21,929 users