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If A is a 3 × 3 invertible matrix, then ...

If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A–1) = (det A)k .

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The correct Answer is:
`k=-1`
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MODERN PUBLICATION-DETERMINANTS-OBJECTIVE TYPE QUESTIONS (Very short answer type question)
  1. |(x^(2)-x+1, x-1),(x+1,x+1)|

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  2. If A is a3x3 matrix, |A| != 0 and |3A|=k|A| , then write the value of ...

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  3. Let A be a square matric of order 3\ xx\ 3 . Write the value of 2A ...

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  4. If A and B are square matrices of same order 3 , such that |A|=2 and A...

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  5. Find the co-factor of the element a(23) of the determinant |{:(5,3,5),...

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  6. Write the minor of 6 in |{:(1,2,3),(4,5,6),(7,8,9):}|

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  7. Write the co-factor of 7 in |{:(4,5,6),(5,6,7),(13,15,17):}|

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  8. For what value of x , is the following matrix singular ? [(3-2x,x+1)...

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  9. For what value of x , the matrix [5-xx+1 2 4] is singular?

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  10. For what value of 'x' the matrix [{:(2-x,3),(-5,-1):}] is not invertib...

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  11. Find the adjoint of the following matrices : [{:(2,-1),(4,3):}]

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  12. Find the adjoint of each of the matrices in questions 1 and 2. [{:(1...

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  13. Find the adjoint of the following matrices : [{:(2,3),(1,4):}]

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  14. If A=[{:(3,1),(2,-3):}], then find |adj.A|.

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  15. If A=[(costheta,-sintheta),(sintheta,costheta)] " then " A^(-1) =?

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  16. If A is a square matrix of order 3 with |A|=9, then write the value of...

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  17. If A is a square matrix with |A|=8, then find the value of |A A'|.

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  18. If A is a 3 × 3 invertible matrix, then what will be the value of k if...

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  19. Write A^(-1) for A=[{:(2,5),(1,3):}].

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  20. if for any 2xx2 square matrix A , A(adjA)=[[8 , 0] , [0 , 8]] then wri...

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