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If A=[(ab,b^(2)),(-a^(2),-ab)] then A is...

If `A=[(ab,b^(2)),(-a^(2),-ab)]` then A is

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Statment - I : |{:(0,ab^(2),ac^(2)),(a^(2)b,0,bc^(2)),(a^(2)c,b^(2)c,0):}|=2a^(3)b^(3)c^(3) Statment - II : |{:(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2)):}|=(a^(3)+b^(3))^(2) Which of the above statement(s) is true ?

If the area of the triangle whose vertices are (b, c) (c, a) (a, b) is p then the area of the triangle whose vertices (ac-b^(2), ab-c^(2))(ab-c^(2), bc-a^(2)) and (bc-a^(2), ac-b^(2)) is

(a xx b)^(2) + (a.b)^(2) =

AAKASH SERIES-MATRICES -ADDITIONAL EXERCISE
  1. A=[(-1,0),(0,2)]impliesA^(3)-A^(2)=

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  2. If A["x y"],B((a,h),(h,b)),C=((x),(y)) then find ABC.

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  3. If A=[(ab,b^(2)),(-a^(2),-ab)] then A is

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  4. If A=((2,-2,-4),(-1,3,4),(1,-2,k)) is an idempotent matrix then find k...

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  5. If A=[(1,1,3),(5,2,6),(-2,-1,-3)] then A is

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  6. If A=[(2,-2,-4),(-1,3,4),(1,-2,-3)] then A is

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  7. If A,B are two idempotent matrices and AB=BA=O then A+B is

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  8. If A is a square matrix then show that A+A^(T) and A A^(T) are symmetr...

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  9. If 5A=[(3,-4),(4,x)] and "AA"^(T)=A^(T)A=I then x=

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  10. If A, B are symmetric matrices of the same order then show that AB-BA ...

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  11. A=[(1+i,2-3i,4),(7+2i,-i,3-2i)], find the conjugate of A.

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  12. If A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,4+5i,2)], then show that A is ...

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  13. If D=|(1,1,1),(1,1+x,1),(1,1,1+y)| for x!=0,y!=0 then D is

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  14. If A=[a(ij)] is a scalar matrix of order nxxn such that a(ij)=k for al...

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  15. If A is a 3xx3 matrix and det(3A)=k(detA) then k=

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  16. If a,b,c are different and |(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(...

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  17. With the usual notation in DeltaABC det|(1,1,1),(sinA,sinB,sinC),(sin^...

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  18. If Delta(1)=|(x,b,b),(a,x,b),(a,a,x)|, Delta(2)=|(x,b),(a,x)| then

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

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  20. If a!=p,b!=q,c!=r and |(p,b,c),(a,q,c),(a,b,r)|=0 then the value of P/...

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