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

Using the properties of determinant, show that : |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]| = 1+a^2+b^2+c^2

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

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

Convert into perfect square. (x^2+x+1/4)-1/4

Convert into perfect square. (x^2+x+1/4)-1/4

Using the properties of determinants, show that abs[[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

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