1. The problem statement, all variables and given/known data Find all real matrices,X, of the form [x 0] [y z] such that X2+3X+2I=0 (I is the identity matrix) 2. Relevant equations 3. The attempt at a solution The only method I know is to work out X2 and then 3X, add to 2I, then equate the corresponding entries with the zero matrix. Have 3 equations with three unknowns and solve. But is there any other method in which I can use to shorten the amount of writing I will have to do?