If square matrices $A^2 + B^2 = 2AB$, then prove that $p_A(x) = p_B(x)$

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2 months ago

# @StackMath

Original problem statement: Let $A, B \in M_n(\mathbb{C})$ such that $A^2 + B^2 = 2AB$. Prove that for any $x \in \mathbb{C}$: $$det(A - xI_n) = det(B-xI_n)$$ Now the first observation, the equal... ...Read More