Without expanding or evaluating show that `|(0,b-a, c-a),( a-b,0,c-b),( a-c ,b-c,0)|=0` .

If Delta=|(0,b-a,c-a),(a-b,0,c-b),(a-c,b-c,0)| , then Delta eqauals

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

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

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

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

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

Without expanding at any state, prove that |((1)/(a),a,bc),((1)/(b),b,ca),((1)/(c ),c,ab)|=0

Without expanding at any state, prove that |(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: |[a-b,b-c,c-a],[ b-c,c-a ,a-b ],[c-a ,a-b,b-c]|=0

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0