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

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

asked in Linear Algebra by Active (1.5k points)   | 97 views

1 Answer

+3 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 (59.6k points)  
selected by
Top Users Jan 2017
  1. Debashish Deka

    8280 Points

  2. sudsho

    5042 Points

  3. Habibkhan

    4716 Points

  4. Vijay Thakur

    4468 Points

  5. Bikram

    4368 Points

  6. saurabh rai

    4212 Points

  7. Arjun

    4052 Points

  8. santhoshdevulapally

    3732 Points

  9. GateSet

    3312 Points

  10. Sushant Gokhale

    3306 Points

Monthly Topper: Rs. 500 gift card

19,138 questions
24,046 answers
52,772 comments
20,283 users