[|[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]|=],[[" (a) "0," (b) "Sigma a," (c) "Sigma ab," (d) "abc]]

|(a - b, b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c)|=0

Evaluate abs([a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c])

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

|(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=

|(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=

Evaluate the following: |[a-b, b-c, c-a],[b-c, c-a, a-b],[c-a, a-b, b-c]|

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

5. Using the properties of determinants, prove that |[a+b,b+c,c+a] , [b+c,c+a,a+b] , [c+a,a+b,b+c]|=2|[a,b,c] , [b,c,a] , [c,a,b]|

Evaluate the following determinants: [[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]]

|{:(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b):}|=8abc