Let $A, B \in M_p(\mathbb{K})$ be two diagonalizable matrices. We assume that $A$ and $B$ commute. Deduce that $E(A + B)$ exists and that $E(A + B) = E(A)E(B) = E(B)E(A)$.
Let $A, B \in M_p(\mathbb{K})$ be two diagonalizable matrices. We assume that $A$ and $B$ commute.
Deduce that $E(A + B)$ exists and that $E(A + B) = E(A)E(B) = E(B)E(A)$.