`|[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 ]|

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

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]]

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

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

Evaluate Delta = {:[ (1,a,bc),( 1,b,ca),(1,c,ab)]:}

Evaluate Delta = {:[ (1,a,bc),( 1,b,ca),(1,c,ab)]:}

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)]