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Prove that |{:(1+a^(2)-b^(2),2ab,-2b),...

Prove that
`|{:(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2)):}|=(1+a^(2)+b^(2))^(3)`

A

`(1+a^(2)+b^(2))^(3)`

B

`(1-a^(2)-b^(2))`

C

`1+a+b`

D

`(1+a+b)^(2)`

Text Solution

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1B MCQ (DETERMINANTS)
  1. IfA=[(1,-2,0),(5,2,3),(1,1,x)] and det(A)=3 Find x=

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  2. If |(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2))|=k the...

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  3. Prove that |{:(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a...

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  4. |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=

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  5. |(1,1,1),(a,b,c),(bc,ca,ab)|=

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  6. |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|=

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  7. |(1,1,1),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

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  8. |(1,1,1),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3))|=

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  9. |(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

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  10. |(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=

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  11. If a,b,c are sides of a triangle and |(a^(2),b^(2),c^(2)),((a+1)^(2),(...

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  12. If A(x)=|(1,1,1),((e^(x)+e^(-x))^(2),(pi^(x)+pi^(-x))^(2),2),((e^(x)-e...

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  13. If a,b,c are sides of a triangle and |(a^(2),b^(2),c^(2)),((a+1)^(2),(...

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  14. |(b^(2)-ab,b-c,bc-ac),(ab-a^(2),a-b,b^(2)-ab),(bc-ac,c-a,ab-a^(2))|=

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  15. |(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2))|=

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  16. |((b+c)^(2),a^(2),bc),((c+a)^(2),b^(2),ca),((a+b)^(2),c^(2),ab)|=

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  17. If A=|(b^(2)c^(2),bc,b+c),(c^(2)a^(2),ca,c+a),(a^(2)b^(2),ab,a+b)| the...

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  18. The determinant Delta=|(a,a+b,a+2b),(a+2b,a,a+b),(a+b,a+2b,a)|=

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  19. If omega is a cube root of unit, then Delta=|(x+1,omega, omega^(2)),(o...

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  20. |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|=

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