|[1,a,bc],[1,b,ca],[1,c,ab]|=.........

Evaluate the following: |[1,1,bc],[1,b,ca],[1,c,ab]|

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

Show without expanding at any stage that: [1/a, a,bc],[1/b,b,ca],[1/c, c, ab]|=0

Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

Without expanding show that |[1/a,1,bc],[1/b,1,ca],[1/c,1,ab]|=0

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

Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

Find the minors and cofactos of each entry of the first column of the matrix A ad hence find the value of the determinant in each case: A = [(1,a,bc),(1,b,ca),(1,c,ab)]