In my linear algebra course I have a problem which goes as follows:

*Suppose A is an nxn matrix over field (R) And J(A) is the jordan form of A.*

*Given **α** belongs to field R, what is the jordan form of **α**A?*

I have worked out, through trial and error, that the jordan form of αA is simply J(A) with the elements (the different eigenvalues) along the diagonal multiplied by **α**.

I couldnt think of a formal proof for this problem, I think it might be some simple characteristic I may have overlooked.

Any help is appreciated
Thanks!