Prove that `Delta = |{:(1,,1,,1),(a,,b,,c),(bc+1^(2),,ac+b^(2),,ab+c^(2)):}|`
`= 2(a-b)(b-c)(c-1)`

Prove the following : |{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-a)

If Delta_(1) = |(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))|, Delta_(2) = |(1,bc,a),(1,ca,b),(1,ab,c) | , then

If Delta_1=|{:(1,1,1),(a,b,c),(a^2,b^2,c^2):}| and Delta_2=|{:(1,bc,a),(1,ac,b),(1,ab,c):}| then : -

Prove that |{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=0

Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

Prove the following : |{:(bc,a,1),(ca,b,1),(ab,c,1):}|=(a-b)(b-c)(a-c)

Prove that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1):}|=1+a^(2)+b^(2)+c^(2) .

Prove that det[[1,a,a^(2)-bc1,b,b^(2)-ca1,c,c^(2)-ab]]=0