Basic question about Pauli Rotations

[ArjSiv]

So it's apparently possible to prove that e^{-iAx} = cos(x)I + isin(x)A given that A^2=I.

What I don't understand is how this is supposed to be derived. Any help would be appreciated as this is driving me nuts and this is probably something that is very easy to prove...

 

[Dr Transport]

Ther are two ways, expand the exponential use the eigenvalues and eigenvectors of the matrix A.

 

[ArjSiv]

Ahh, I knew I was missing something stupid. I didn't realize that A^{2n}A = A.

Thanks :)