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If A and B are square matrices of size n...

If A and B are square matrices of size `nxxn` such that `A^(2)-B^(2)=(A-B)(A+B)`, then which of the following will be always true?

A

either of A or B is a zero matrix

B

either of A or B is an identity matrix

C

`A=B`

D

`AB=BA`

Text Solution

Verified by Experts

The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1A MCQ (ALGEBRA OF MATRICES)
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  2. If A,B are two idempotent matrices and AB=BA=O then A+B is

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  3. If A and B are square matrices of size nxxn such that A^(2)-B^(2)=(A-B...

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  4. If a=[(1,2,3),(2,4,5),(x,5,6)] and A^(T)=A then x=

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  5. If A=[(x,1,4),(-1,0,7),(-4,-7,0)] such that A'=-A then x=

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  6. If A=[(0,1,-2),(-1,0,3),(2,-3,0)] then A+A^(T)=

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  7. If A=[(1,-1,2),(2,1,-3),(-2,1,2)],B=[(2,1,0),(2,-3,1),(1,1,-1)] then (...

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  8. If A=[(1,2,3)],B=[(2),(3),(-1)] then (A+B^(T))^(T)=

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  9. If A=[(1),(0),(-1)],B=[(2,3,2)] then (A+B^(T))^(T)=

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  10. If A=[(1,-2,3),(-4,2,5)],B=[(1,3),(-1,0),(2,4)] then 2A+3B'=

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  11. If A=[(1,5,3),(2,4,0),(3,-1,-5)] and B=[(2,-1,0),(0,-2,5),(1,2,0)] the...

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  12. If A+2B=[(2,-4),(1,6)], B^T=[(1,2),(0,-1)] then A=

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  13. If 3A+4B'=[(7,-10,17),(0,6,31)],2B-3A'=[(-1,18),(4,-6),(-5,-7)] then B...

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  14. If A=[(i,0),(0,-i)], then A A'=

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  15. If A=[(0,i),(-i,0)] then "AA"^(T)=

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  16. If A=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] then "AA"^(T)=

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  17. If A=[(cos alpha, sin alpha),(-sin alpha, cos alpha)], then (2A)(1/4A...

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  18. If A=[(2,0,-1),(1,1,2),(-1,1,0)] then "AA"^(T)=

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  19. If A=[(2,3),(5,-7)] then (A')^(2)=

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  20. If A=[(0,-1),(1,0)] then

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