Exponent of polynomials (of matrices) 
$A$ is a matrix over $\mathbb R$ (reals).
Prove that for every $f,g\in \mathbb R[x]$, $\displaystyle e^{f(A)}\times e^{g(A)} = e^{f(A)+g(A)}$

I tried using the sigma writing but got stuck
(I wrote $f(x)=\sum a_ix^i$, $g(x)=\sum bix^i$ and then started to develop the left part of the equation and then I got stuck ..)
Any suggestions ? thanks guys

You should know that for square matrices $A,B$ the following holds:
$AB=BA \implies e^Ae^B=e^{A+B}$.
Can you prove that if $P,Q$ are polynomials and $A$ a square matrix, $P(A)Q(A)=Q(A)P(A)$ ?
