" (ii) "|[b+c,a-b,a],[c+a,b-c,b],[a+b,c-a,c]|=[pi11" at "pi+a_(n)],[-3ab-a^(3)-b^(2)-c^(3)]

Prove: |[b+c ,a-b ,a], [c+a, b-c ,b], [a+b, c-a, c]|=3a b c-a^3-b^3-c^3

|(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(3abc-a^(3)-b^(3)-c^(3))

|(1,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=a^(3)+b^(3)+c^(3)-3ab

det[[a,b,ca-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc

Prove the identities: |[a, b, c],[ a-b,b-c,c-a],[ b+c,c+a, a+b]|=a^3+b^3+c^3-3a b c

Show that |[a_(1),b_(1),-c_(1)],[-a_(2),-b_(2),c_(2)],[a_(3),b_(3),-c_(3)]|=|[a_(1),b_(1),c_(1)],[a_(2),b_(2),c_(2)],[a_(3),b_(3),c_(3)]|

Prove the identities: det[[a-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abcdet[[a-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc

Show that [[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]] = 3(a+b+c)(ab+bc+ca)

The value of the determinant |(bc,ac,ab),(a,b,c),(a^(3),b^(3),c^(3))| is a)(a + b + c) b)a + b + c -ab c) (a^(2) - b^(2))(b^(2) - c^(2)) (c^(2) - a^(2)) d) a^2+b^2+c^2

Prove that |b+c a-b a c+a b-c b a+b c-a c|=3a b-a^3-b^3-c^3dot