" 5."quad 77[[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]|" on "H=(1)/(8)

det[[b+c,a-c,a-bb-c,c+a,b-ac-b,c-a,a+b]]=8abc

|(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)|=

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]|

Prove the identities: |[a, b-c,c-b],[ a-c, b, c-a],[ a-b,b-a, c]| =(a+b-c)(b+c-a)(c+a-b)

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]|

Prove that : |[a+b+c,-c,-b],[-c, a+b+c, -a],[-b,-a,a+b+c]|= 2(a+b)(b+c)(c+a)

Prove that |[a+b+c, -c, -b],[-c, a+b+c, -a],[-b, -a, a+b+c]|=2(a+b)(b+c)(c+a)

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

Show that |(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b)|=8abc