If a,b,c are all distinct and `|[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]|` =0, show that abc(ab+bc+ac) = a+b+c

If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]|=0, show that a b c(a b+b c+c a)=a+b+c

If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]|=0, show that a b c(a b+b c+c a)=a+b+c

if a, b, c, are all distinct and |{:(a,a^3,a^4-1),(b,b^3,b^4-1),(c,c^3,c^4-1):}|=0 , show that abc(ab+bc+ca)=a+b+c.

If A=[[0 ,c,-b],[-c, 0, a],[ b, -a, 0]] and B=[[a^2, ab, ac],[ ab, b^2 , bc],[ ac ,bc, c^2]] , show that A B=B A=O_3xx3 .

Show that [[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]] = 3(a+b+c)(ab+bc+ca)

If a,b,are distinct,show that [[1,1,1a,b,ca^(3),b^(3),c^(3)]]=(b-c)*(c-a)*(a-b)(a+b+c)