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

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

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

show that det[[a-b,b-c,c-ab-c,c-a,a-bc-a,a-b,b-c]]=0

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

If Delta=det[[0,b-a,c-aa-b,0,c-ba-c,b-c,0]], then Delta

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

Show that |[0,c,b] , [c,0,a] , [b,a,0]|^2=|[b^2+c^2, ab, ac] , [ab, c^2+a^2, bc] , [ac, bc, a^2+b^2]|

Prove that : |{:(0,a-b,a-c),(b-a,0,b-c),(c-a,c-b,0):}|=0

Evaluate |[0,c,b] , [c,0,a] , [b,a,0]| hence show that |[0,c,b] , [c,0,a] , [b,a,0]|^2= |[b^2+c^2,ab,ac] , [ab,c^2+a^2,bc] , [ca,bc,a^2+b^2]|=4a^2b^2c^2