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If A; B are invertible matrices of the s...

If A; B are invertible matrices of the same order; then show that `(AB)^-1 = B^-1 A^-1`

A

`(A^(-1)xxB^(-1))`

B

`(AxxB^(-1))`

C

`(A^(-1)xxB)`

D

`(B^(-1)xxA^(-1))`

Text Solution

Verified by Experts

The correct Answer is:
D
`(AB)^(-1)=B^(-1),A^(-1)`
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RS AGGARWAL-SYSTEM OF LINEAR EQUATIONS-Objective Questions
  1. Find a matrix X such that X.[(3,2),(1,-1)]=[(4,1),(2,3)].

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

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

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

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

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

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

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

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

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

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

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

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

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  14. If matrices A and B anticommute then

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

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

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

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

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  19. If |A|=3 and A^(-1)=[(3,-1),((-5)/3,2/3)] then adjA=?

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  20. If A is an invertible matrix and A^(-1)=[(3,5),(5,6)] then A=?

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