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If A is a non singular square matrix, th...

If A is a non singular square matrix, then the false statement among the following is

A

`"Adj A"=|A|A^(-1)`

B

`("Adj A")^(-1)=(A)/(|A|)`

C

`"det "(A^(-1))=("det A")^(-1)`

D

`"Adj A = O if A = I"`

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-MATRICES -INVERSE OF A MATRIX- EXERCISE - I
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  3. If [(x,y^(3)),(2,0)]=[(1, 8),(2,0)] then [(x,y),(2,0)]^(-1)=

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  4. If A [(2,2),(-3,2)],B=[(0,-1),(1,0)] then (B^(-1)A^(-1))^-1=

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  5. Adj[(1,0,2),(-1,1,-2),(0,2,1)]=[(5,a,-2),(1,1,0),(-2,-2,b)]implies[(a,...

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  6. If A=((cosx,sinx,0),(-sinx,cosx,0),(0,0,1))=f(x) then A^(-1)=

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  7. The matrix having the same matrix as its inverse is

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  8. 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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  9. The inverse of [(3,5,7),(2,-3,1),(1,1,2)] is

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  10. If A is a non singular square matrix, then the false statement among t...

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  11. If A is an invertible matrix of order n, then the determinant of adj A...

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  12. If A is 3xx3 matrix and det A=-2 then |"Adj A"|=

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  13. If a is a 3xx3 matrix and |"Adj A"|=16 then |A|=

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  14. If |(1,-1,x),(1,x,1),(x,-1,1)| has no inverse, then the real value of ...

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  15. If [(0,1,a),(1,a,0),(a,0,1)] is invertible then a!=

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  16. If A is a nonzero square matrix of order n with det(I+A)!=0 and A^(3)=...

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  17. If |A|!=0 and (A-2I) (A-3I) = 0 then A^(-1)=

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  18. If det (A(3xx3))=6, then det (Adj 2A) =

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

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  20. If Delta=|{:(a(1),b(1),c(1)),(a(2),b(2),c(2)),(a(3),b(3),c(3)):}| then...

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