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If A, B are two n xx n non-singular matr...

If A, B are two `n xx n` non-singular matrices, then (1) AB is non-singular (2) AB is singular (3) `(AB)^(-1)=A^(-1) B^(-1)` (4) `(AB)^(-1)` does not exist

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RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. If A=[[a, b],[ c ,d]] , then a d j\ A is (a) [[-d,-b],[-c, a]] (b) [[d...

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  2. If A is a singular matrix, then adj A is a. Singular b. non singular...

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  3. If A, B are two n xx n non-singular matrices, then (1) AB is non-singu...

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  4. If A=[(a , 0) ,(0 ,a)] , then the value of |a d j\ A| is ?

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  5. If A= [ [1, 2] , [-1, 1]] , then det (a d j\ A)) is ?

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  6. If B is a non-singular matrix and A is a square matrix, then det (B^(-...

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  7. For any 2xx2 matrix, if A\ (a d j\ A)=[[10 ,0 ],[0 ,10]] , then |A| is...

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  8. If A^5=O such that A^n != I for 1 <= n <= 4, then (I - A)^-1 is equal ...

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  9. If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists ...

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  10. If for the matrix A ,\ A^3=I , then A^(-1)=(a)A^2 (b) A^3 (c) A (d) no...

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  11. If Aa n dB are two square matrices such that B=-A^(-1)B A ,t h e n(A+B...

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  12. If A=[(2 ,0 ,0),( 0 ,2 ,0),( 0 ,0 ,2)] , then A^5= (a) 5A (b) 10 A (c...

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  13. For non-singular square matrix A ,\ B\ a n d\ C of the same order th...

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  14. The matrix [(5 ,1 ,0), (3 ,-2 ,-4 ), (6 ,-1 ,-2b)] is a singular matri...

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  15. If d is the determinant of a square matrix A of order n , then the ...

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  16. If A is a matrix of order 3 and |A|=8 , then |a d j\ A|= (a) 1 (b)...

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  17. If A^2-A +I = 0, then the inverse of A is: (A) A+I (B) A (C) ...

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  18. If A and B are invertible matrices, which of the following statemen...

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  19. If A is a square matrix such that A^2 = I, then A^(-1) is equal to (i...

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  20. Let A=[(1, 2), (3,-5)] and B=[(1, 0), (0, 2)] and X be a matrix such t...

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