`|[(b+c)^2,ab,ca],[ab,(a+c)^2,bc],[ac,bc,(a+b)^2]|=2abc(a+b+c)^3`

Prove that |[(a+b)^(2),ca,bc],[ca,(b+c)^(2),ab],[bc,ab,(c+a)^(2)]|=2abc(a+b+c)^(3)

|{:(a^2,ab,ac),(ab,b^2,bc),(ca,bc,c^2):}|= ?

|[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]|=|[a,b,c],[b,c,a],[c,a,b]|^2

If A=[[a^2,ab,ac],[ab,b^2,bc],[ac,bc,c^2]] and a^2+b^2+c^2=1, then A^2

Prove that identities: |[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]|=(a b+b c+a c)^3

Prove that identities: |[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]|=(a b+b c+a c)^3

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 .

Using the properties of determinants show that : |[[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]]|=(ab+bc+ca)^3