Without expanding or evaluating show that `|[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|=0`

Without expanding or evaluating show that |0b-ac-aa-b0c-ba-cb-c0|=0

Without expanding or evaluating show that det[[a-b,0,c-ba-c,b-c,0]]=0

Without expanding determinant show that |(0,a,b),(-a,0,c),(-b,-c,0)|=0

Without expanding the determinant prove that: |0b-c-b0a c-a0|=0

Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

Show that det[[0,b-a,c-aa-b,0,c-ba-c,b-c,0]]=0

Show without expanding at any stage that: [0,a,-b],[-a,0,-c],[b,c,0]|=0

Using the property of determinants and without expanding, prove that: |[a-b,b-c,c-a],[ b-c,c-a ,a-b ],[c-a ,a-b,b-c]|=0

Without expanding the determinant prove the following. |[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]|=0

Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+b|=0 .