Your idea is good
Let Y be P^-1XP
From part A you know that Y must be of diagonal structure
Find P and you will get the general form of X
part A(i managed to solve it):
X is a variable of
are different rational numbers.
solve XD=DX for X.
so i get
so for both side to be equal X must be of diagonal structure
every member must be zero except the diagonal
because the lambda values are given as different.
part B(the one that i dont understand):
what is the solution space of XA=AX (use part A)??
XPDP^-1=PDP^-1X (multiplying by p from the right)
XPD=PDP^-1XP (multiplying by p^-1 from the left)
another thing i could find is the eigen values of the matrix
i can substitute A by X but whats to do next??