Show that `|[-1,b,c],[a,-1,c],[a,b,-1]|= (a+1)(b+1)(c+1)(a/(a+1)+b/(b+1)+c/(c+1)-1)`

det[[ Show that ,,-1,b,ca,-1,ca,b,-1]]=(a+1)(b+1)(c+1)((a)/(a+1)+(b)/(b+1)+(c)/(c+1)-1)

Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

|(1+a,b,c),(a,1+b,c),(a,b,1+c)|=

By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^3,b^3,c^3]| = (a-b)(b-c)(c-a)(a+b+c)

Show that |(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)

Show that |{:(bc,b-c,1),(ca,c+a,1),(ab,a+b,1):}|=(a-b)(b-c)(c-a)

Show that |{:(bc,b+c,1),(ca,c+a,1),(ab,a+b,1):}|=(a-b)(b-c)(c-a)

Show that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)

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