1. The problem statement, all variables and given/known data Prove that for all complex two by two matrices, they will be upper triangular matrices (edit: i think what is meant by upper triangular matrices is that PAP^-1 will be upper triangular matrices - the wording of the question i was given was a little misleading it seems) 2. Relevant equations A=PDP^-1 3. The attempt at a solution The way I tried to do it was to show that A will have n distinct eigenval, whereby I let A=[a b c d] i found the eigenvals for that. then and for the case a=d, tried to show that the eigenvec are not linearly independent. However, this is the correct way to do it? or is there a much easier solution to this question?