[" 11.Using properties of determinants,Prove that "],[qquad |[1+a,1,1],[1,1+b,1],[1,1,1+c]|=ab+bc+ca+abc]

Using properties of determinants prove that : |(1+a,1,1),( 1,1+b,1),(1,1,1+c)| =abc +bc +ca +ab

Using properties of determinant show that : |(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc+ab+bc+ca

Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1],[1,1,1+c]]=abc(1+1/a+1/b+1/c)

Using the properties of determinants, show that |(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc+bc+ca+ab

Using properties of determinants , prove that |{:(1,a,bc),(1,b,ca),(1,c,ab):}|=(a-b)(b-c)(c-a)

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

Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

Prove that {:|(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc+bc+ca+ab

Using the properties of determinants show that : |[[1,1,1],[a^2,b^2,c^2],[a^3,b^3,c^3]]|=(a-b)(b-c)(c-a)(ab+bc+ca) .