Using properties of determinant, prove that `|{:(a^(2)+2a, 2a+1, 1), (2a+1, a+2, 1), (3, 3, 1):}|=(a-1)^(3)`

Using properties of determinants, prove that |(a^2+2a, 2a+1,1), (2a+1, a+2, 1), (3,3,1)| = (a-1)^3

Using properties of determinants, prove that |(a^2+2a, 2a+1,1), (2a+1, a+2, 1), (3,3,1)| = (a-1)^3

Using properties of determinants, prove that 3 2 (a 1) 3 3 1 2a 1 a 2 1 a 2a 2a

Using properties of determinant, prove that |{:( 1,a,a^(2)),(a^(2) , 1,a),( a,a^(2),1):}|=(a^(3) -1)^(2)

Using properties of determinant prove that |(a^(2)+1, ab, ac),(ab, b^(2)+1, bc),(ca, cb,c^(2)+1)|=(1+a^(2)+b^(2)+c^(2)) .

Using properties of determinants, prove that : |{:(a^(2)+1,ab,ac),(ba,b^(2)+1,bc),(ca,cb,c^(2)+1):}|=a^(2)+b^(2)+c^(2)+1

Using properties of determinants, prove 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)

Using properties of determinants prove that |(1,1, 1+3x),(1+3y,1,1),(1, 1+3z,1)| =9(3xyz+xy+yz+zx)

Using properties of determinants, prove that |[(a+1)(a+2),a+2,1],[(a+2)(a+3),a+3,1],[(a+3)(a+4),a+4,1]|=-2

Using properties of determinants. Prove that |[1 ,1+p,1+p+q],[2, 3+2p,4+3p+2q],[3, 6+3p, 10+6p+3q]|=1