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|[a,b,c],[a^(2),b^(2),c^(2)],[a^(3),b^(3...

|[a,b,c],[a^(2),b^(2),c^(2)],[a^(3),b^(3),c^(3)]|=abc(b-c)(c-a)(a-b).

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Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-b)(b-c)(c-a)

Match the following from List - I to List - II {:("List-I","List-II"),((I)|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=,(a)(a-b)(b-c)(c-a)),((II)|{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3)):}|=,(b)(a-b)(b-c)(c-a)abc),((III)|{:(1,1,1),(a,b,c),(a^(3),b^(3),c^(3)):}|=,(c)(a-b)(b-c)(c-a)(a+b+c)):}

Prove that |[[a,b,c],[a^2,b^2,c^2],[a^3,b^3,c^3]]|= abc (a-b)(b-c)(c-a)

Prove that |[a,b,c] , [a^2,b^2,c^2] , [a^3,b^3,c^3]|= abc(a-b)(b-c)(c-a)

Show that |[a,b,c],[a^2,b^2,c^2],[a^3,b^3,c^3]|=abc(a-b)(b-c)(c-a)

|{:(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=abc(a-b)(b-c)(c-a)

Prove the following identities : |{:(a,a^(2),a^(3)),(b,b^(2),b^(3)),(c,c^(2),c^(3)):}|=abc(a-b)(b-c)(c-a) .

Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(c^(2),2ac-b^(2),a^(2)),(b^(2),a^(2),2ab-c^(2)):}|=(a^(3)+b^(3)+c^(3)-3abc)^(2)