`|{:(b+c,a,1),(c+a,b,1),(a+b,c,1):}|=0`

|{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Without expanding show that |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Without expanding show that : |(a,b+c,1),(b,c+a,1),(c,a+b,1)|=0

|{:(a-b,1,a),(b-c,1,b),(c-a,1,c):}|=|{:(a,1,b),(b,1,c),(c,1,a):}|

|{:(-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)

|{:(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)):}|=0

If a,b,c are in G.P. then the value of |(a,b,a+b),(b,c,b+c),(a+b,b+c,0)|= (A) 1 (B) -1 (C) a+b+c (D) 0

If a,b,c are in G.P. then the value of |(a,b,a+b),(b,c,b+c),(a+b,b+c,0)|= (A) 1 (B) -1 (C) a+b+c (D) 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

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