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## Homework Statement

a.) If A

^{2}= I, what are the possible eigenvalues of A?

b.) If this A is 2 by 2, and not I or -I, find its trace and determinant.

c.) If the first row is (3,-1), what is the second row?

## Homework Equations

None was given, but I think:

1. det(A) = 1 for A

^{2}= I or A

^{-1}= A

We're studying about Matrix diagonalization and the topic is called "Diagonalization of a Matrix". The equation S[tex]\Lambda[/tex]S

^{-1}= A is supposed to be relevant.

## The Attempt at a Solution

a.) I got the possible eigenvalues to be: [tex]\lambda[/tex]

_{1}x [tex]\lambda[/tex]

_{2}x ... x [tex]\lambda[/tex]

_{n}= 1

b.) tr(A) = [tex]\lambda[/tex] + [tex]1/\lambda[/tex]

det(A) = 1

c.) This is where I'm stuck... I know I'm supposed to use the equation det(A) = 1 but there are two unknowns and I only know one equation. I was going to use the equation S[tex]\Lambda[/tex]S

^{-1}= A but then I realized that I need the eigenvectors and I can't find the eigenvectors since I don't know the whole matrix.

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