What Does Trace(p^4-p^3) Equal for a 2x2 Complex Matrix with Given Properties?

[ajayguhan]

Homework Statement

Let P be 2x2 complex matrice such that trace(p)=1 det(p)=-6 then trace(p^4-p^3) equals what...?

Homework Equations

Is there any formula for trace(A^n)

The Attempt at a Solution

Let the two eigen values be a,b

a+b=1 a*b= -6 solving we get a=(1+i√23)/2 and b =(1-i√23)/2

Trace(p^4-p^3)=trace(p^4)-trace(p^3)

 

[Mark44]

Homework Statement

Let P be 2x2 complex matrice such that trace(p)=1 det(p)=-6 then trace(p^4-p^3) equals what...?

Homework Equations

Is there any formula for trace(A^n)

The Attempt at a Solution

Let the two eigen values be a,b

a+b=1 a*b= -6 solving we get a=(1+i√23)/2 and b =(1-i√23)/2

Trace(p^4-p^3)=trace(p^4)-trace(p^3)

Trace identities: http://en.wikipedia.org/wiki/Trace_(linear_algebra)