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If A and B are two matrices such that ra...

If A and B are two matrices such that rank of A = m and rank of B = n, then

A

rank (AB)= mn

B

`"rank "(AB)gt" rank " (A)`

C

`" rank "(AB)gt " rank "(B)`

D

`"rank "(AB) lt min ("rank A, rank B")`

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Exercise
  1. If A is an orthogonal matrix, then

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

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

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

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

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  6. Let A be a matrix of rank r. Then,

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  7. Let A=[a(ij)](mxxn) be a matrix such that a(ij)=1 for all I,j. Then ,

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  8. If A is a non-zero column matrix of order mxx1 and B is a non-zero row...

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  9. The rank of the matrix {:[(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,5)]:}, ...

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  10. If A is an invertible matrix, then "det" (A -1) is equal to

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  11. If A and B are two matrices such that rank of A = m and rank of B = n...

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  12. If A=[3 4 2 4] , B=[-2-2 0-1] , then (A+B)^(-1) (a) is a skew-symmetr...

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  13. Let A=[a0 0 0a0 0 0a] , then A^n is equal to [a^n0 0 0a^n0 0 0a] (b) [...

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  14. If A=[[costheta,sintheta],[-sintheta,costheta]],then Lim(x>oo)1/nA^n i...

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  15. If A=[[1, 2, x], [0 ,1 ,0],[ 0, 0, 1]] and B=[[1,-2,y],[0, 1, 0 ],[0...

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  16. If A=[{:(,1,a),(,0,1):}] then find underset(n-oo)(lim)(1)/(n)A^(n)

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  17. If the matrix {:[(a,b),(c,d)]:} is commutative with matrix {:[(1,1),(...

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  18. If {:A=[(1,0),(k,1)]andB=[(0,0),(k,0)]:} such that A^100-I=lambdaB," ...

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  19. If matrix A has 180 elements, then the number of possible orders of A ...

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  20. A 3xx3 matrix A, with 1st row elements as 2,-1,-1 respectively, is mod...

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