If A and B are non - singular matrices of order three such that `adj(AB)=[(1,1,1),(1,alpha, 1),(1,1,alpha)] and |B^(2)adjA|=alpha^(2)+3alpha-8`, then the value of `alpha` is equal to

If A=[{:(alpha,0),(1,1):}]and B=[{:(1,0),(2,1):}] such that A^(2)=B , then what is the value of alpha ?

If A=[{:(alpha,0),(1,1)] and B=[{:(1,0),(2,1):}] such that A^(2)=B then what is the value of alpha ?

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

If tan A=(alpha^(2)-alpha)/(alpha^(2)-alpha+1) and tan B=(1)/(2 alpha^(2)-2 alpha+1) then (A+B) equals to

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))

Let alpha be a root of the equation x ^(2) + x + 1 = 0 and the matrix A = ( 1 ) /(sqrt3) [{:( 1,,1,,1),( 1,, alpha ,, alpha ^(2)), ( 1 ,, alpha ^(2),, alpha ^(4)):}] then the matrix A ^( 31 ) is equal to :

Let alpha be a root of the equation x ^(2) + x + 1 = 0 and the matrix A = ( 1 ) /(sqrt3) [{:( 1,,1,,1),( 1,, alpha ,, alpha ^(2)), ( 1 ,, alpha ^(2),, alpha ^(4)):}] then the matrix A ^( 31 ) is equal to :

If alpha is a roots of equation x^(2)+x+1=0 and A=(1)/(sqrt3)[{:(,1,1,1),(,1,alpha,alpha^(2)),(,1,alpha^(2),alpha):}] then A^(31) equal to: