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For any two matrices A and B , we have...

For any two matrices A and B , we have

A

AB=BA is always true

B

AB=BA is never true

C

sometimes AB=BA and sometimes AB `ne `BA

D

whenever AB exists , then BA exists

Text Solution

Verified by Experts

The correct Answer is:
C
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RS AGGARWAL-SYSTEM OF LINEAR EQUATIONS-Objective Questions
  1. If A is a 3-rowed square matrix and |A|=4 then |adjA|=?

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  2. If A is a 3-rowed square matrix and |A|=5 then |adjA|=?

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  3. For any two matrices A and B , we have

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  4. Find a matrix X such that X.[(3,2),(1,-1)]=[(4,1),(2,3)].

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  5. If A is an invertible square matrix then |A^(-1)|=?

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  6. If A; B are invertible matrices of the same order; then show that (AB)...

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  7. If A and B are two nonzero square matrices of the same order such that...

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  8. If A is square matrix such that |A| ne 0 and A^2-A+2I=O " then " A^(-1...

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  9. If A=[(1,lambda,2),(1,2,5),(2,1,1)] is not invertible then lambda=?

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  10. If A=[(costheta,-sintheta),(sintheta,costheta)] " then " A^(-1) =?

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  11. If A=[(ab,b^2),(-a^2,-ab)] then matrix A is (A) scalar (B) involuntary...

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  12. If A=[[2,-2,-4],[-1,3,4],[1,-2,-3]] then A is 1) an idempotent matrix ...

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  13. If A is singular then A(adjA)=?

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  14. if for any 2*2 square matrix A , A(adjA)=[[8 , 0] , [0 , 8]] then writ...

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  15. If A=[(-2,3),(1,1)] then |A^(-1)|=?

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  16. If A=[{:(3,1),(7,5):}], find x and y such that A^(2)+xI=yA.

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  17. If matrices A and B anticommute then

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  18. If A=[{:(2,5,),(1,3,):}] , find adj A.

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  19. If A=[(3,-4),(-1,2)] and B is a square matrix of order 2 such that AB=...

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  20. If A; B are invertible matrices of the same order; then show that (AB)...

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