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If A `=[{:( alpha , a ),( beta , b),( gamma, c):}]` then ` (A)A^(T) ` is

A

a non-singular matrix

B

a singular matrix

C

an identity matrix

D

none of these

Text Solution

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The correct Answer is:
B
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FIITJEE-MATRICES -ASSIGNMENT PROBLEM (OBJECTIVE) (Level-I)
  1. If I=[{:(,1,0),(,0,1):}], J=[{:(,0,1),(,-1,0):}]and B=[{:(,cos theta,s...

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  2. If I=[{:(,1,0),(,0,1):}], J=[{:(,0,1),(,-1,0):}]and B=[{:(,cos theta,s...

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  3. If A={:[(i,i),(-i,i)] and B= [{:( 1,-1),(-1,1) :}] then A^(8) equal...

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  4. Let Aa n dB be two 2xx2 matrices. Consider the statements A B=O A+Oo...

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  5. The number of 3xx3 matrices with entries from the set {-1, 0,1} such t...

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  6. If A and B are symmetric matrices of order n(A!=B) then (A) A+B is ske...

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  7. The number of all the matrices A= [adj ]1le 1i,le 4 such that a(ij) =...

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  8. Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(...

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  9. The values of x for which the matrix [[x+a,b,c],[a,x+b,c],[a,b,x+c]] ...

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  10. If Aa n dB are square matrices of the same order and A is non-singular...

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  11. The inverse of a skew symmetric matrix is

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  12. If [{:( 1,2,3),(1,3,5),(1,5,12):}] then adj (adj A) is

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  13. Let A be a square matrix of order 3 such that transpose of inverse of ...

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  14. If A =[{:( alpha , a ),( beta , b),( gamma, c):}] then (A)A^(T) is

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  15. If A and B are non-singular square matrices of same order then adj(AB)...

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  16. If A^(k)=0 (null matrix) for some value of k, then l+A+A^(2)+…A^(k-1) ...

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  17. If A =({:( 1,1,1),( 1,omega ^(2) , omega ),( 1 ,omega , omega ^(2)) :...

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  18. Matrices of order 3xx3 are formed by using the elements of the set A={...

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  19. Statement -1 :if A = [a(ij) ](nxxn) and a(ij) =( i^(2) +j^(2) -ij) (I...

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  20. Statement 1: F a,b,c are real positive numbers with abc =1 and AA^(T) ...

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