Evaluate the following: `|[1,a, b c],[1,b, c a],[1,c, a b]|`

Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|

Using properties of determinant show that: |[1 , a , bc] , [1 , b , ca] , [1 , c , a b]|=(a-b)(b-c)(c-a)

Evaluate the following |(1, 1, 1),(a^2,b^2,c^2),(a^3,b^3,c^3)|

Evaluate Delta=|1a b c1b c a1c a b|

Using the property of determinants and without expanding, prove that: |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b, c(a+b)]|=0

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .

Evaluate: |(1,a ,a^2), (1,b,b^2) ,(1,c,c^2)| .

By using properties of determinants. Show that: (i) |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=(a-b)(b-c)(c-a) (ii) |[1, 1, 1],[a, b, c],[ a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a+b+c)

If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,ab, c]| , then