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Which of the following statements is fal...

Which of the following statements is false:

A

if `|A|=0` then `|adjA|=0`

B

adjoint of a diagonal matrix of order `2xx2` is a diagonal matrix

C

product of two upper trianglular 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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DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1C MCQ (INVERSE MATRIX)
  1. If A=[(cos x, sin x),(-sin x, cos x)] and AdjA=[(1,0),(0,1)] then the ...

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  2. If a is a square matrix, then adjA^(T)-(adjA)^(T)=

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  3. If A, B are two invertible matrices of same type then (AB)^(-1)=

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  4. Which of the following statements is false:

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

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  6. If the matrix A=[(1,2),(3,4)] then I+A+A^(2)+………… up to infinitey

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

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

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  9. A is a square matrix satisfying the equation A^(2)-4A-5I=O. Then A^(-1...

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  10. If for a matrix A,A^(2)+I=O where I is the indentity matrix, then A=

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  11. If A=[(a,b),(0,c)] then A^(-1)+(A-aI)(A-cI)=

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  12. If A=[(2,-1,1),(-1,2,-1),(1,-1,2)] then A^(2)=

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  13. If A=[(2,1,1),(1,3,1),(1,2,1)] then A^(T)=

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  14. Let A and B be two invertible matrices of order 3×3. If det (ABA^T)=8 ...

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  15. If A = [(a+ib,c+id),(-c+id,a-ib)], a^(2)+b^(2)+c^(2)+d^(2) =1, then fi...

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  16. If A and B are square matrices of order 3 such that detA=-1,detB=3 th...

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  17. The inverse of a symmetric (if it exists) is

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  18. The inverse of a skew symmetric matrix. (if it exists ) is

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  19. The inverse of a skew symmetric matrix of odd order is

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

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