if `A=[[a,b],[b,a]]` and `A^2 =[[alpha,beta],[beta,alpha]]` then

If A=[[a , b] ,[ b , a]] A^(2)=[[alpha , beta] ,[ beta , a]] then

If A={:[(a,b),(b,a)]:} and A^(2)={:[(alpha,beta),(beta,alpha)]:} such that beta=Kab . Then the value of K will be___

If x=a+b, y=a alpha + b beta and z= alpha beta + b alpha , where alpha and beta are complex cube roots of unity, then xyz=

If alpha, beta, gamma are the roots of x^3+a x^2+b=0 then the value of [[alpha , beta , gamma],[beta , gamma , alpha],[gamma , alpha , beta]] is

If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,beta,gamma],[beta,gamma,alpha],[gamma,alpha,beta]|=0, alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha , and gamma+alpha-beta .

If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,beta,gamma],[beta,gamma,alpha],[gamma,alpha,beta]|=0, alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha , and gamma+alpha-beta .

If sin alpha+sin beta=a and cos alpha+cos beta=b then tan((alpha-beta)/(2)) is equal to

If sin alpha+sin beta=a and cos alpha-cos beta=b then tan((alpha-beta)/(2))=