If `f(alpha)=[[1,alpha,alpha^2],[alpha,alpha^2,1],[alpha^2,1,alpha]]` then find the value of `f(3^(1/3))`

If f(alpha) = |{:(1,alpha,alpha^2),(alpha,alpha^2,1),(alpha^2,1,alpha):}| , then find the value of f(3^(1/3)) .

If f(alpha)=|{:(1,alpha,alpha^(2)),(alpha,alpha^(2),1),(alpha^(2),1,alpha):}| , then f(root(3)(3)) is equal to

Prove that |{: (1,alpha,alpha^2), (alpha,alpha^2, 1),(alpha^2, 1,alpha) :}|=-(1-alpha^3)^2

If 1,alpha,alpha^2,alpha^3,......,alpha^(n-1) are n n^(th) roots of unity, then find the value of (2011-alpha)(2011-alpha^2)....(2011-alpha^(n-1))

If 1,alpha,alpha^(2),alpha^(3),......,alpha^(n-1) are nn^(th) roots of unity,then find the value of (2011-alpha)(2011-alpha^(2))....(2011-alpha^(n-1))

|[(1+alpha)^(2),(1+2 alpha)^(2),(1+3 alpha)^(2)(2+alpha)^(2),(2+2 alpha)^(2),(2+3 alpha)^(2)(3+alpha)^(2),(3+2 alpha)^(2),(3+3 alpha)^(2) Find the value of alpha

Let F(alpha)=[[cos alpha,-sin alpha,0sin alpha,cos alpha,00,0,1]], where alpha in R Then (F(alpha))^(-1) is equal to F(alpha^(-1)) b.F(-alpha) c.F(2 alpha)d.-[[1,11,0]]

If a variable takes the discrete value alpha+4alpha-(7)/(2),alpha-(5)/(2),a-3,alpha-2,alpha+(1)/(2),alpha-(1)/(2)alpha+5(alpha>0), then the median of these values: