Trying to solve a proof for Linear Algebra:

for a in the set of complex numbers, e^a = lim k-> ∞ (1 + a/k)^k

Establish the matrix analog for any A in the set of real nxn square matrices

e^A = lim k->∞ (I + A/k)^k

I started off by trying the following:

A = P D P^-1

A^k = P D^k P^-1

e^At = P e^D^kt P^-1

not sure where to go from here or if this is the right thought process, I would appreciate any help I can get!

Thanks