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If A and B are symmetric matrices of the...

If A and B are symmetric matrices of the same order then (AB-BA) is always

A

a symmetric matrix

B

a skew symmetric matrix

C

a zero matrix

D

an identity matrix

Text Solution

Verified by Experts

The correct Answer is:
B
Given A'=A and B'=B
`therefore(AB-BA)'=(AB)'-(BA)'=(B'A'-A'B')=(BA-AB)=-(AB-BA)`
`therefore(AB-BA)` is skew symmetric
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RS AGGARWAL-SYSTEM OF LINEAR EQUATIONS-Objective Questions
  1. If A and B are square matrics of the same order then (A+B)^2=?

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  2. If A and B are square matrics of the same order then (A-B)^2=?

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  3. If A and B are symmetric matrices of the same order then (AB-BA) is al...

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  4. Matrices A and B will be inverse of each other only if (A) A B" "="...

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  5. If A; B are non singular square matrices of same order; then adj(AB) =...

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  6. If A is a 3-rowed square matrix and |A|=4 then |adjA|=?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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