Prove `|[1,x,x^2],[x^2,1,x],[x,x^2,1]|=(1-x^3)^2`

Using properties of determinants, prove the following: |[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2

Using properties of determinants, prove the following: |[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2

Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

Using properties of determinants prove the following. abs[[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

Prove that |(1,x,x^2),(x^2,1,x),(x,x^2,1)|=(1-x^2) .

Prove that |(1,x,x^2),(x^2, 1,x),(x,x^2 ,1)| =(1-x^3)^2

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,x,x^2),(x^2,1,x),(x,x^2,1):}|=(1-x^3)^2

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