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If the matrix AB is a zero matrix, then ...

If the matrix AB is a zero matrix, then which one of the following is correct ?

A

A = O or B = O

B

A = O and B `!= `O

C

It is not necessary that either A = O or B = O

D

All the above statements are wrong

Text Solution

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The correct Answer is:
C
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MOTION-MATRICES -Exercise - 1
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  2. <b>a. Row Matrix :</b> Matrix of order 1 xx m is called <b>row matrix<...

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

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  4. Which relation is true for A =[(2,-1),(-1,2)] and B=[(1,4),(-1,1)] (1)...

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  5. If A=[(a,b),(b,a)]and A^(2)=[(alpha,beta),(beta,alpha)], then -

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  6. If A and B are square matrices of order n xx n such that A^2-B^2=(A-B)...

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  7. If A=[(ab,b^2),(-a^2,-ab)], then A is

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  8. A = [[2,-1],[-7,4]] & B =[[4,1],[7,2]] then B^TA^T is :

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  9. If a non-singular matrix and A^(T) denotes the tranpose of A, then

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  10. If A is skew-symmetric matrix, then trace of A is

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  11. If A and B are symmetric matrices, then A B A is

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  12. If A is a skew-symmetric matrix and n is an even natural number,...

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  13. Which one of the following is wrong ?

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  14. [{:(,1,2),(,2,1):}],[{:(,1,2),(,2,1):}]

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  15. If A=[(costheta,-sintheta,0),(sintheta,costheta,0),(0,0,1)], then adj ...

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  16. If A is a squqre matrix such that A^(2)=l, then A^(-1) is equal to

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  17. If A=[(3,-3,4),(2,-3,4),(0,-1,1)], then :

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  18. If A = [[1,2],[3,-5]] and B=[[1,0],[0,2]] and X is a matrix such that ...

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  19. Given A=[(1,3),(2,2)],I=[(1,0),(0,1)]. If A-lambdaI is a singular mat...

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  20. From the matrix equation AB = AC we can conclude B = C provided that

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