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If A=[{:(3,4),(5,6),(7,8):}] and B = [{:...

If `A=[{:(3,4),(5,6),(7,8):}] and B = [{:(3,5,7),(4,6,8):}]`. Then which one of following is correct ?

A

B is the inverse of A

B

B is the adjoint of A

C

B is the transpose of A

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C

We have,
`A=[(3,4),(5,6),(7,8)]`
`A^(T)=[(3,5,7),(4,6,8)]=B`
`therefore" B is the transpose of A"`
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NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
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  2. Inverse of diagonal matrix is (A) a diagonal matrix (B) symmetric (C) ...

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  3. If A=[{:(3,4),(5,6),(7,8):}] and B = [{:(3,5,7),(4,6,8):}]. Then which...

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  4. If the sum of the matrices [{:(x),(x),(y):}],[{:(y),(y),(z):}]and[{:(z...

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  5. If the matrix AB is a zero matrix, then which one of the following is ...

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  6. If the matrix [{:(alpha,2,2),(-3,0,4),(1,-1,1):}] is not invertible, t...

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  7. The value of the determinant |{:(x^(2),1,y^(2)+z^(2)),(y^(2),1,z^(2)+x...

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  8. A square matrix [a(ij)] such that a(ij)=0 for i ne j and a(ij) = k whe...

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  9. If A and B are two non-singular square matrices such that AB = A, then...

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  10. What is the value of the minor of the element 9 in the determinant |{:...

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  11. The roots of the equation |{:(" "1,t-1," "1),(t-1," "1," "1),(" "1," "...

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  12. The value of the determinant |{:(m,n,p),(p,m,n),(n,p,m):}|

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  13. The determinant of a orthogonal matrix is :

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  14. If D is determinant of order 3 and D' is the determinant obtained by r...

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  15. Consider the following statements : 1. A matrix is not a number 2....

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  16. Consider the following statements : 1. The product of two non-zero m...

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  17. Consider the following statements : 1. The matrix ({:(1,2,1),(a,2a,1...

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  18. The cofactor of the element 4 in the determinant |{:(1,2,3),(4,5,6),(7...

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  19. If A is a square matrix of order 3 with |A|ne 0, then which one of the...

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  20. If A =({:(i,0),(0,-i):}),B=({:(0,-1),(1,0):}),C=({:(0,i),(i,0):}) wher...

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