" 16."|[1,a,bc],[1,b,ca],[1,c,ab]|=|[1,a,a^(2)],[1,b,b^(2)],[1,c,c^(2)]|

Prove that |[1,a,bc] , [1,b,ca], [1,c,ab]|=|[1,a,a^2] , [1,b,b^2] , [1,c,c^2]|

Evaluate [[1,a,bc],[1,b,ca],[1,c,ab]]-[[1,a,a^2],[1,b,b^2],[1,c,c^2]]

Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,c^2]]

1,bc,b+c1,ca,c+a1,ab,a+b]|=det[[1,a,a^(2)1,b,b^(2)1,c,c^(2)]]

Show without expanding at any stage that: [a,a^2,bc],[b,b^2,ca],[c,c^2,ab]|=|[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Without expanding the determinant, Prove that |[a,a^2, bc],[b,b^2,ca],[c,c^2,ab]|= |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

|[a,a^(2),bc],[b,b^(2),ca],[c,c^(2),ab]|=|[1,a^(2),a^(3)],[1,b^(2),b^(3)],[1,c^(2),c^(3)]|

Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]| = |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

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

Without expanding prove that, |{:(1,bc,b+c),(1,ca,c+a),(1,ab,a+b):}|=|{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|