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Prove that |{:(1, a, a^(2)-bc),(1, b, b...

Prove that `|{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=0`

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The value of the determinant |{:(1,a, a^(2)-bc),(1, b, b^(2)-ca),(1, c, c^(2)-ab):}| is…..

Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0

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 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 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 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 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)) ]:}

If D=|(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab)| , then D is -

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 |{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|