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

Without expanding at any stage, prove that |{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

Without expanding the determinant, prove that |(a,a^2,bc),(b,b^2,ca),(c,c^2,ab)|=|(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3)|

Without expanding at any stage, prove that |(a-b,1,a),(b-c,1,b),(c-a,1,c)| = |(a,1,b),(b,1,c),(c,1,a)|

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

Delta = |(1//a,1,bc),(1//b,1,ca),(1//c,1,ab)|=

Without expanding determinant at any stage evaluate |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|

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

Show without expanding at any stage that: |[(a-1)^2, a^2+1, a],[(b-1)^2, b^2+1,b],[(c-1)^2, c^2+1, c]|=0

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