If `|[1,a,bc] , [1,b,ac] , [1,c,ab]|=lambda|[a^2,b^2,c^2] , [a,b,c] , [1,1,1]|` then `lambda` is equal to

Prove that |[1,a,bc] , [1,b,ca], [1,c,ab]|=|[1,a,a^2] , [1,b,b^2] , [1,c,c^2]|

If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,ab, c]| , then

Evaluate [[1,a,bc],[1,b,ca],[1,c,ab]]-[[1,a,a^2],[1,b,b^2],[1,c,c^2]]

Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,c^2]]

If |(a^2,b^2,c^2),((a+lambda)^2,(b+lambda)^2,(c+lambda)^2),((a-lambda)^2,(b-lamda)^2,(c-lambda)^2)|=klambda|(a^2,b^2,c^2),(a,b,c),(1,1,1)|lambda!=0 then k is equal to :

If |(a^2,b^2,c^2),((a+lambda)^2,(b+lambda)^2,(c+lambda)^2),((a-lambda)^2,(b-lamda)^2,(c-lambda)^2)|=klambda|(a^2,b^2,c^2),(a,b,c),(1,1,1)|lambda!=0 then k is equal to : (A) 4 lambda abc (B) -4 lambda abc (C) 4 lambda^2 (D) -4 lambda^2

If |(a^2,b^2,c^2),((a+lambda)^2,(b+lambda)^2,(c+lambda)^2),((a-lambda)^2,(b-lamda)^2,(c-lambda)^2)|=klambda|(a^2,b^2,c^2),(a,b,c),(1,1,1)|lambda!=0 then k is equal to : (A) 4 lambda abc (B) -4 lambda abc (C) 4 lambda^2 (D) -4 lambda^2

If |(a^(2), b^(2), c^(2)),((a+lambda)^(2), (b+lambda)^(2), (c+lambda)^(2)),((a-lambda)^(2), (b-lambda)^(2), (c-lambda)^(2))|=klambda|(a^(2), b^(2),c^(2)),(a,b,c),(1,1,1)|,lambda ne 0 then k is equal to

Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(a-b)(b-c)(c-a)

if [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=lambda a^2b^2c^2 then find the value of lambda