Show that the determinant `|{:(1,a,a^(2)),(a^(2),1,a),(a,a^(2),1):}|` is a perfect square.

Prove that: |[1, a ,a^2],[a^2, 1 ,a],[a, a^2, 1]| is a perfect square.

Without expanding show that the determinant |(1,a,a^2),(-1,2,4),(1,x,x^2)| has a factor (X-a)

Show that the following determinant is a perfact square : |{:(1,a,a^2),(a^2,1,a),(a,a^2,1):}|

Show that the determinant is perfect square: ,a^(2),2a,11,a^(2),2a2a,1,a^(2)]|

Show that the following determinant is a perfect square |[1,a,a^2],[a^2,1,a],[a,a^2,1]|

show that (3a+2b-c+d)^(2)-12a(2b-c+d) is a perfect square .

Prove that |[x^2,2x,1],[1,x^2,2x] , [2x,1,x^2]| is a perfect square

For what value of k,(4-k)x^(2)+2(k+2)x+(8K+1) is a perfect square.

For what value of 'y', x^(2)=(1)/(12)x-y^(2) is a perfect square ?

By using properties of determinants , show that : {:[( 1,x,x^(2) ),( x^(2) ,1,x) ,( x,x^(2), 1) ]:} =( 1-x^(3)) ^(2)