Problems Set

Problem. Let $A, B \in M_n(k)$ such that $A^2+B^2=2AB$. Show that

I. det $A$ = det $B$,

II. $A, B$ have the same characteristic polynomials.

Solution.

Matrices A,B satisfying A^2 + B^2 = 2AB have the same characteristic polynomials

$\text{Unfinished.}$ 12/02/2025