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Consider the following statements with r...

Consider the following statements with respect to the square matrices A and B of same order
I. A and B are non-zero and `AB = 0 rArr` either |A|=0 or |B|=0
II. `AB=0 rArr A=0" or B=0`
Which of the above statements is/are correct ?

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Text Solution

Verified by Experts

The correct Answer is:
D
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PUNEET DOGRA-DETERMINANTS -PREV YEAR QUESTIONS
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  2. If a, b and c are real numbers, then the value of the determinant |(1-...

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  3. Consider the following statements with respect to the square matrices ...

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  4. The value of |(1,1,1),(1,1+x,1),(1,1,1+y)| is

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  5. Consider the following statements I. Determinant is a square matrix....

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  6. If |(a,b,0),(0,a,b),(b,0,a)| = 0, then which one of the following is c...

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  7. If a ne b ne c all are positive, then the value of determinant |(a,b,c...

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  8. If any two adjacent rows or columns of a determinant are interchanged ...

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  9. The determinant of a skew symmetric matrix of odd order is

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  10. If C(ij) is the cofactor of the element a(ij) of the determinant |{:(2...

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  11. What is the value of the determinant |(1,bc,a(b+c)),(1,ca,b(c+a)),(1,a...

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

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  13. Consider the following statements I. A matrix is not a number. II....

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  14. The roots of the equation |(1,t-1,1),(t-1,1,1),(1,1,t-1)| = 0 are

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  15. The value of the determinant |(m,n,p),(p,m,n),(n,p,m)|

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  16. If each element in a row of a determinant is multiplied by the same fa...

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  17. If two rows (or column) are identical or Proportional the value of the...

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  18. If |(8,-5,1),(5,x,1),(6,3,1)| = 2, then what is the value of x ?

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  19. If A = ((1,2),(2,3))and = ((1,0),(1,0)), then what is the value of det...

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  20. What is the value of |(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))| ?

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