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If A is an invertible matrix, then which...

If A is an invertible matrix, then which of the following is correct

A

`A^(-1)` is multivalued

B

`A^(-1)` is singular

C

`(A^(-1))^T ne (A^T)^(-1)`

D

`absA ne 0`

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA-MATRICES-Exercise
  1. Let A and B be matrices of order 3 xx 3. If AB = 0, then which of the ...

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  2. Which of the following is incorrect ?

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  3. If A is an invertible matrix, then which of the following is correct

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  4. Which of the following is/are incorrect? (i) adjoint of a symmetri...

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  5. If {:[(alpha,beta),(gamma,-alpha)]:} is to be the square root of two-r...

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

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  7. If A=[a(ij)](mxxn) is a matrix of rank r then (A) rltmin{m,n} (B) rlem...

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  8. If In is the identity matrix of order n, then rank of In is

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  9. IfA=[a(ij)](mxxn) is a matrix of rank r and B is a square submatrix of...

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  10. The rank of a null matrix is

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  11. If A=[a(ij)](mxxn) is a matrix and B is a non-singular square submatri...

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  12. Which of the following is correct ?

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  13. If a square matrix A is orthogonal as well as symmetric, then

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  14. Let A be a skew-symmetric of odd order, then absA is equal to

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  15. Let A be a skew-symmetric matrix of even order, then absA

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  16. If A is an orthogonal matrix, then

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  17. Let A be a non-singular square matrix of order n. Then; |adjA| = |A|^(...

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  18. Let A=[a(ij)](nxxn) be a square matrix of order 3 such that |A|=-7 an...

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  19. If A is a non-singlular square matrix of order n, then the rank of A i...

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  20. If A is a matrix such that there exists a square submatrix of order r ...

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