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Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+...

Prove that `[[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+b^2+b^4, 1+b c+b^2c^2],[ 1+a c+a^2c^2, 1+b c+b^2c^2, 1+c^2+c^4]]=(a-b)^2(b-c)^2(c-a)^2`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+...

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  2. If |[1 1 1];[a b c];[ a^3b^3c^3]|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b...

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  3. Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+...

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  4. The determinant |[y^2,-x y, x^2],[a, b, c],[ a ', b ', c ']| is equal ...

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  5. If x , y , z are in A.P. , then the value of the determinant |[a+2,...

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  6. Prove that |{:((b+x)(c+x),,(c+x)(a+x),,(a+x)(b+x)),((b+y)(c+y) ,,(c+y)...

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  7. If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is ...

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  8. Factorize the following |[3,a+b+c,a^3+b^3+c^3],[a+b+c,a^2+b^2+c^2,a^4+...

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  9. Let {D1, D2, D3 ,Dn} be the set of third order determinant that can be...

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  10. If g(x)=(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of de...

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  11. If the equation 2x+3y+1=0,3x+y-2=0, and a x+2y-b=0 are consistent, t...

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  12. If w is a complex cube root of unity, then value of =|[a1+b1w, a1w^2+b...

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  13. Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), ...

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  14. Which of the following has/have value equal to zero? |[8, 2, 7],[ 12, ...

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  15. If f(x),g(x) and h(x) are three polynomials of degree 2, then prove th...

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  16. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are i...

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  17. Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|=(a+b+c)(a^2+b^2...

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  18. In triangle A B C , if |[1, 1, 1],[cot(A/2),cot(B/2),cot(C/2)],[tan(B/...

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  19. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

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  20. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

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