`|[1,a ,a+b],[1,b,b+c],[1,c,c+a]|=0`

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

Show without expanding at any stage that: [1,a,b+c],[1,b,c+a],[1,c,a+b]|=0

If D=[[1,a,b],[1,b,c],[1,c,a]] , then [[a,b,c],[b,c,a],[1,1,1]] =

Prove that |[1+a,1, 1], [1,1+b,1], [1, 1, 1+c]|=a b c(1+1/a+1/b+1/c)=a b c+b c+c a+a b

|[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0

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

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

Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c,c^2)|

Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]] =0

prove |[1, b c, a(b+c)],[ 1, c a, b(c+a)],[ 1, a b, c(a+b)]|=0