" Find the factor of "|[a,b,c],[a^(2),b^(2),c^(2)],[bc,ca,ab]|

Find the value of |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|

Prove the following : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=|{:(a,a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=(ab+bc+ca)(a-b)(b-c)(c-a) .

Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]] =(b-c)(c-a)(a-b)(bc+ca+ab)

Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c-a)(ab+bc+ca)

Prove that: 1/(bc+ca+ab)|[a, b, c],[a^2, b^2, c^2], [bc, ca, ab]|=(b-c),(c-a),(a-b)

Find the value of : |(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab)|

Show that the determinant |(a^(2)+b^(2)+c^(2),bc+ca+ab,bc+ca+ab),(bc+ca+ab,a^(2)+b^(2)+c^(2),bc+ca+ab),(bc+ca+ab,bc+ca+ab,a^(2)+b^(2)+c^(2))| is always non - negative

Prove that abs((a,b,c),(a^2,b^2,c^2),(bc,ca,ab))=(a-b)(b-c)(c-a)(ab+bc+ca)