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Let A and B be matrices of order 3 xx 3....

Let A and B be matrices of order `3 xx 3.` If `AB = 0,` then which of the following can be concluded?

A

`A=Oand B=O`

B

`absA=OandabsB=O`

C

either absA=Oor absB=O`

D

`A=Oor B=O`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Exercise
  1. If A and B are two matrices such that A+B and AB are both defind, then

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  2. If a matrix A is such that 3\ A^3+2\ A^2+5\ A+I=0 , then A^(-1) is equ...

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  3. Let A and B be matrices of order 3 xx 3. If AB = 0, then which of the ...

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

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

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  6. If [[alpha, beta], [gamma, -alpha]] is to be square root of two-rowed ...

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  7. If for matrix A,A^(2)+l=0, where l is the identity matrix, then A equa...

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  8. If A=[a(ij)](mxxn) is a matrix of rank r then (A) r=min{m,n} (B) rlemi...

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

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  10. A=[a(ij)](mxxn) is a square matrix, if

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  11. The rank of a null matrix is

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

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  13. Which of the following is correct ?

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

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

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

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  17. If A is an orthogonal matrix, then

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

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  19. Let A=[a(ij)](n xxn) be a square matrix and let c(ij) be cofactor of...

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

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