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Which of the following statements is fal...

Which of the following statements is false:

A

if |A| = 0, then |adj A| = 0

B

adjoint of a diagonal matrix of order `3xx3` is a diagonal matrix

C

product of two upper triangular matrices is an upper triangular matrix

D

adj (AB) = adj (A) adj (B)

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The correct Answer is:
D
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AAKASH SERIES-MATRICES -INVERSE OF A MATRIX- EXERCISE - II
  1. If 3A=[(1,2,2),(2,1,-2),(-2,2,-1)] then A^(-1)=

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  2. If A is non - singular and A^(2)-5A+7I=0 then I =

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  3. If A is non Singular and (A-2I)(A-4I)=0 then 1/6A+4/3A^(-1)=

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  4. A square nonsingular matrix satisfies A^(2)-A+2I=0 then A^(-1)=

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  5. If A!=A^(2)=I then |I+A|=

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  6. If A is a 3xx3 matrix and B is its Adjoint matrix. If the determinent ...

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  7. If A is 4xx4 matrix and |2A|=64,B="Adj A" then |"Adj B"|=

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  8. If A!=I is an idempotent matrix, then A is a

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  9. If A is an orthogonal matrix then |A| is

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  10. If A and B are two square matrices such that B=-A^(-1)BA then (A+B)^(2...

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  11. The value of a third order determinant is 11 then the value of the squ...

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  12. A and B are square matrices of order 3xx3, A is on orthogonal matrix a...

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  13. Which of the following statements is false:

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  14. Let A be 2xx2 matrix. Statement : adj(adjA)=A Statement -2: |adjA|=|A|

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  15. If the product of the matrix B=[(2,6,4),(1,0,1),(-1,1,-1)] with a matr...

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  16. If A is any square matrix of order 'n' Observe the following list {:...

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  17. Statement 1 : If A is nxxn matrix then |"adj (adj(adjA))|=|A|^((n-1)^...

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  18. The element of third row second column of the inverse of A=[(2,-4,-2),...

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  19. If |{:(a(1),b(1),c(1)),(a(2),b(2),c(2)),(a(3),b(3),c(3)):}|=5, then th...

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  20. If P=[(1, alpha, 3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix A...

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