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## Homework Statement

If A is a diagonal matrix with the diagonal entries a1, a2, ...., an, use the power series to prove that exp(At) is a diagonal matrix with the entries exp(a1t), exp(a2t), ....., exp(ant).

## Homework Equations

## The Attempt at a Solution

I can prove that A is diagonalizable with T-1 AT=D, but I'm not sure how to begin the proof using the power series as a method. My book does not discuss this and any insight would be greatly appreciated, thanks!