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Show that: |[1,x,x^2],[x^2,1,x],[x,x^2,...

Show that: ` |[1,x,x^2],[x^2,1,x],[x,x^2,1]|=(1-x^3)^2 `

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By using properties of determinants.Show that: det[[1,x,x^(2)x^(2),1,xx,x^(2),1]]=(1-x^(3))^(2)

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

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

If a ne 0 and a ne 1, show that |{:(x+1,x,x),(x,x+a,x),(x,x,x+a^(2)):}|=a^(3)[1+x((a^(3)-1))/(a^(2)(a-1))].

If a ne 0 and a ne 1, show that |{:(x+1,x,x),(x,x+a,x),(x,x,x+a^(2)):}|=a^(3)[1+x((a^(3)-1))/(a^(2)(a-1))].

If a ne 0 and a ne 1, show that |{:(x+1,x,x),(x,x+a,x),(x,x,x+a^(2)):}|=a^(3)[1+x((a^(3)-1))/(a^(2)(a-1))].

If a ne 0 and a ne 1, show that |{:(x+1,x,x),(x,x+a,x),(x,x,x+a^(2)):}|=a^(3)[1+x((a^(3)-1))/(a^(2)(a-1))].

If a ne 0 and a ne 1, show that |{:(x+1,x,x),(x,x+a,x),(x,x,x+a^(2)):}|=a^(3)[1+x((a^(3)-1))/(a^(2)(a-1))].

If a ne 0 and a ne 1, show that |{:(x+1,x,x),(x,x+a,x),(x,x,x+a^(2)):}|=a^(3)[1+x((a^(3)-1))/(a^(2)(a-1))].