1. The problem statement, all variables and given/known data a.) If A2 = 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? 2. Relevant equations None was given, but I think: 1. det(A) = 1 for A2 = 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. 3. 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.