`|{:(" "1+a^2-b^2," "2ab," "-2b),(" "2ab,1-a^2+b^2," "2a),(" "2b," "-2a,1-a^2-b^2):}|=(1+a^2+b^2)^3`

The value of the determinant |(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2))| is equal to

By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: 2ab;1-a^2+b^2; 2a: 2b;-2a;1-a^2-b^2|=(1+a^2+b^2)^3

prove that , |{:(2ab,a^2,b^2),(a^2,b^2,2ab),(b^2,2ab,a^2):}|=-(a^3+b^3)^2

If a, b and c are in G.P. then prove that 1 a 2 - b 2 + 1 b 2 = 1 b 2 - c 2 . 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

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)) |:}

Prove that |[2ab,a^2,b^2],[a^2,b^2,2ab],[b^2,2ab,a^2]|=-(a^3+b^3)^2 .

|{:(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 a^(2) + b^(2) + c^(2) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to

Factorise : 1-a^(2)+2ab-b^(2)

Prove that |[1, 1, 1]; [a, b, c]; [ bc+a^2, ac+b^2, ab+c^2]| = 2(a-b)(b-c)(c-a)