Prove that : `|{:(0,a-b,a-c),(b-a,0,b-c),(c-a,c-b,0):}|=0`

witout expanding at any stage Prove that |{:(0,,a,,-b),(-a,,0,,-c),(b,,c,,0):}| =0

Prove that det[[a-b,b-c,c-ab-c,c-a,a-bc-a,a-b,b-c]]=0

Value of determinant |{:(0,b,-c),(-b,0,a),(c,-a,0):}| is equal to

Using the property of determinants and without expanding,prove that: det[[a-b,b-c,c-ab-c,c-a,a-bc-a,a-b,b-c]]=0

If a+b+c=0 the one root of |{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}| =0 is

If |(a,-b,a-b-c),(-a,b,-a+b-c),(-a,-b,-a-b+c)| - kabc = 0 (a != 0, b != 0, c != 0) then what is the value of k ?

Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

If a, b, c are complex numbers, then the determinant Delta = |(0,-b,-c),(bar(b),0,-a),(bar(c),bar(a),0)| , is

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