1. The problem statement, all variables and given/known data A n × n-matrix A satisfies the equation A2 = A. (a) List all possible characteristic polynomials of A. (b) Show that A is similar to a diagonal matrix 2. Relevant equations 3. The attempt at a solution A2 = A so, A2 - A = 0 A(A-I) = 0 Our minimal polynomial is x2 - x = m(x) Our eigenvalues are 0 and 1, and since in our minimal polynomial each one has a multiplicity of 1, A is similar to a diagonal matrix consisting of n jordan blocks with either 1's or 0's on the diagonal and 0 everywhere else since we have an nxn matrix and n jordan blocks. So I've proved part (b) first. For part (a) we don't know how many times each eigenvalue occurs in the characteristic polynomial, so p(t) = ta(t-1)b where a,b=0,1,2,...,n. Is this correct?