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The determinants |(1,a,bc),(1,b,ca),(1,c...

The determinants `|(1,a,bc),(1,b,ca),(1,c,ab)| and |(1,a,a^2),(1,b,b^2),(1,c,c^2)|` are identically equal.

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The determinants |{:(1,a, bc),(1, b, ca),(1, c, ab):}| " and "|{:(1,a, a^(2)),(1, b, b^(2)),(1, c, c^(2)):}| are not identically equal.

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

1,bc,b+c1,ca,c+a1,ab,a+b]|=det[[1,a,a^(2)1,b,b^(2)1,c,c^(2)]]

det[[1,a,a^(2)+bc1,b,b^(2)+ac1,c,c^(2)+ab]] is equal to

Delta=det[[1,a,bc1,b,ca1,c,ab]]

The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^2) (B) a^3+b^3+c^3-3abc (C) (a-b)(b-c)(c-a) (D) 0

(1)/(a),a^(2),bc(1)/(b),b^(2),ca(1)/(c),c^(2),ab]|