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## Homework Statement

exp^\prime(0)B=B for all n by n matrices B.

## Homework Equations

exp(A)= \sum_{k=0}^\infty A^k/k!

## The Attempt at a Solution

Obviously I want to calculate the limit of some series, but I don't know what series to calculate. I wanted to try \lim_{h \to 0}(\exp(hB)-exp(0))/h, but I'm not sure if that's right. I feel like that's just taking the directional derivative, and not the entire derivative of exp. I'm just a little lost right now, and all would I like is not even solution but just help in pointing me in the right direction as to which limit I should be expliciting calculating.