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A = [{:( a,b,c) ,( b,c,a),(c,a,b) :}] if...

` A = [{:( a,b,c) ,( b,c,a),(c,a,b) :}]` if trace (A)= 9 and a,b , c are positive integers such that ab + bc + ca = 26 Let` A_1 `denotes the adjoint of matrix A , `A_2 ` represent adjoint of `A_1 ….` and so on if value of det` ( A_4) ` is M, then

A

`M= 3^(48)`

B

` M= 3^(24)`

C

last two digits of M is 61

D

last three digits of M is 861

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The correct Answer is:
A, C
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Knowledge Check

  • Let a_1,a_2,a_3,a_4,a_5 be a G.P. Of positive real numbers such that A.M. Of a_2 and a_4 is 117 and G.M. Of a_2 and a_4 is 108. Then A.M. Of a_1 and a_5 is :

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  • Let a=2hati+3hatj-6hatk, b=2hati-3hatj+6hatk and c=-2hati+3hatj+6hat(k), Let a_1 be the projection of a on b and a_2 be the projection of a_1 and c . Then Q. a_1, b is equal to

    A
    `-41`
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    `-(41)/(7)`
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  • If A, B and C are square matrices of order 3 and |A|=2, |B|=3 and |C|=4 , then the value of |3(adjA)BC^(-1)| is equal to (where, adj A represents the adjoint matrix of A)

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    B
    `(27)/(4)`
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