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|[1,x,x^(2)],[x^(2),1,x],[x,x^(2),1]|=(1...

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

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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

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 f(x)=det[[x-2,(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+2)^(3) then coefficient of x in f(x), is ]]

If D(x)=det[[(x-1),(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+1)^(3) then the coefficient of x in D(x), is ]]

[[3x^(2),3x,1x^(2)+2x,2x+1,12x+1,x+2,1]]=(x-1)^(3)